KILLED proof of input_Nr2gIw9QgT.trs # AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 75 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 20 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 64.7 s] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 291 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 16.4 s] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 16.1 s] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (28) CpxWeightedTrs (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTypedWeightedTrs (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) NarrowingProof [BOTH BOUNDS(ID, ID), 272 ms] (34) CpxTypedWeightedCompleteTrs (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms] (36) CpxRNTS (37) InliningProof [UPPER BOUND(ID), 465 ms] (38) CpxRNTS (39) SimplificationProof [BOTH BOUNDS(ID, ID), 9 ms] (40) CpxRNTS (41) CompletionProof [UPPER BOUND(ID), 0 ms] (42) CpxTypedWeightedCompleteTrs (43) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms] (44) CpxRNTS (45) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (46) CdtProblem (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CpxRelTRS (53) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (54) CpxTRS (55) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CpxWeightedTrs (57) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CpxTypedWeightedTrs (59) CompletionProof [UPPER BOUND(ID), 0 ms] (60) CpxTypedWeightedCompleteTrs (61) NarrowingProof [BOTH BOUNDS(ID, ID), 2763 ms] (62) CpxTypedWeightedCompleteTrs (63) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 29 ms] (64) CpxRNTS (65) InliningProof [UPPER BOUND(ID), 926 ms] (66) CpxRNTS (67) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CpxRNTS (69) CompletionProof [UPPER BOUND(ID), 0 ms] (70) CpxTypedWeightedCompleteTrs (71) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (72) CpxRNTS (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 77 ms] (142) CdtProblem (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 74 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 61 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 56 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 67 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 84 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 83 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 90 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 109 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 90 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (214) CdtProblem (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (226) CdtProblem (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 18 ms] (228) CdtProblem (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (232) CdtProblem (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (234) CdtProblem (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 ms] (238) CdtProblem (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 22 ms] (240) CdtProblem (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (242) CdtProblem (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (244) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) a__U12(tt, V2) -> a__U13(a__isNat(V2)) a__U13(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0) -> tt a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U13(X)) -> a__U13(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2) -> U12(X1, X2) a__isNat(X) -> isNat(X) a__U13(X) -> U13(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatKind(X) -> isNatKind(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) a__U12(tt, V2) -> a__U13(a__isNat(V2)) a__U13(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0') -> tt a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0') -> tt a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__plus(N, 0') -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U13(X)) -> a__U13(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0') -> 0' a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2) -> U12(X1, X2) a__isNat(X) -> isNat(X) a__U13(X) -> U13(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatKind(X) -> isNatKind(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) a__U12(tt, V2) -> a__U13(a__isNat(V2)) a__U13(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0) -> tt a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U13(X)) -> a__U13(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2) -> U12(X1, X2) a__isNat(X) -> isNat(X) a__U13(X) -> U13(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatKind(X) -> isNatKind(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0) -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0) -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0) -> c42 S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0) -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0) -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0) -> c42 K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_2, A__U13_1, A__U21_2, A__U22_1, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c1, c2_2, c3, c4, c5, c6_2, c7, c8, c9, c10_1, c11, c12_2, c13_2, c14, c15_1, c16, c17, c18_3, c19_2, c20, c21, c22_2, c23_1, c24, c25_3, c26_4, c27, c28_2, c29_2, c30_1, c31_2, c32_2, c33_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c40, c41_1, c42 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0) -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0) -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0) -> c42 The (relative) TRS S consists of the following rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0') -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0') -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0') -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0') -> c42 The (relative) TRS S consists of the following rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0') -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0') -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0') -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0') -> c42 a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c:c1 tt :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c :: c2:c3 -> c17:c18:c19:c20 -> c:c1 A__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c2:c3 a__isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNAT :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c17:c18:c19:c20 c1 :: c:c1 c2 :: c4:c5 -> c17:c18:c19:c20 -> c2:c3 A__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c4:c5 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c6:c7 c6 :: c8:c9 -> c17:c18:c19:c20 -> c6:c7 A__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c10:c11 c10 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c10:c11 MARK :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c11 :: c10:c11 A__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c12:c13:c14 c12 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 A__PLUS :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c25:c26:c27 mark :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c13 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 c14 :: c12:c13:c14 A__AND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c15:c16 c15 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c15:c16 c16 :: c15:c16 0' :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c17 :: c17:c18:c19:c20 plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c18 :: c:c1 -> c15:c16 -> c21:c22:c23:c24 -> c17:c18:c19:c20 a__and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNATKIND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c21:c22:c23:c24 s :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c19 :: c6:c7 -> c21:c22:c23:c24 -> c17:c18:c19:c20 c20 :: c17:c18:c19:c20 c21 :: c21:c22:c23:c24 c22 :: c15:c16 -> c21:c22:c23:c24 -> c21:c22:c23:c24 c23 :: c21:c22:c23:c24 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 c25 :: c10:c11 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 c26 :: c12:c13:c14 -> c15:c16 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c27 :: c25:c26:c27 U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c28 :: c:c1 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c29 :: c2:c3 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c30 :: c17:c18:c19:c20 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c31 :: c4:c5 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c32 :: c6:c7 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c33 :: c8:c9 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c34 :: c10:c11 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c35 :: c12:c13:c14 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c36 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c37 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c38 :: c15:c16 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c39 :: c21:c22:c23:c24 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c40 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c41 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c42 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 a__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c:c11_43 :: c:c1 hole_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U412_43 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c2:c33_43 :: c2:c3 hole_c17:c18:c19:c204_43 :: c17:c18:c19:c20 hole_c4:c55_43 :: c4:c5 hole_c6:c76_43 :: c6:c7 hole_c8:c97_43 :: c8:c9 hole_c10:c118_43 :: c10:c11 hole_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c429_43 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 hole_c12:c13:c1410_43 :: c12:c13:c14 hole_c25:c26:c2711_43 :: c25:c26:c27 hole_c15:c1612_43 :: c15:c16 hole_c21:c22:c23:c2413_43 :: c21:c22:c23:c24 gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43 :: Nat -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43 :: Nat -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 gen_c21:c22:c23:c2416_43 :: Nat -> c21:c22:c23:c24 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__U11, A__U12, a__isNat, A__ISNAT, A__U21, A__U31, MARK, A__U41, A__PLUS, mark, A__AND, a__and, a__isNatKind, A__ISNATKIND, a__U11, a__U12, a__U21, a__U31, a__U41, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 a__isNat < A__U11 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U31 A__U11 = MARK A__U11 = A__U41 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNATKIND a__isNat < A__U12 A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U31 A__U12 = MARK A__U12 = A__U41 A__U12 = A__PLUS A__U12 = A__AND A__U12 = A__ISNATKIND a__isNat < A__U21 a__isNat < A__PLUS a__isNat = mark a__isNat = a__and a__isNat = a__isNatKind a__isNat = a__U11 a__isNat = a__U12 a__isNat = a__U21 a__isNat = a__U31 a__isNat = a__U41 a__isNat = a__plus A__ISNAT = A__U21 A__ISNAT = A__U31 A__ISNAT = MARK A__ISNAT = A__U41 A__ISNAT = A__PLUS A__ISNAT = A__AND a__and < A__ISNAT a__isNatKind < A__ISNAT A__ISNAT = A__ISNATKIND A__U21 = A__U31 A__U21 = MARK A__U21 = A__U41 A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNATKIND A__U31 = MARK A__U31 = A__U41 A__U31 = A__PLUS A__U31 = A__AND A__U31 = A__ISNATKIND MARK = A__U41 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNATKIND A__U41 = A__PLUS mark < A__U41 A__U41 = A__AND A__U41 = A__ISNATKIND A__PLUS = A__AND a__and < A__PLUS A__PLUS = A__ISNATKIND mark = a__and mark = a__isNatKind mark = a__U11 mark = a__U12 mark = a__U21 mark = a__U31 mark = a__U41 mark = a__plus A__AND = A__ISNATKIND a__and = a__isNatKind a__and = a__U11 a__and = a__U12 a__and = a__U21 a__and = a__U31 a__and = a__U41 a__and = a__plus a__isNatKind < A__ISNATKIND a__isNatKind = a__U11 a__isNatKind = a__U12 a__isNatKind = a__U21 a__isNatKind = a__U31 a__isNatKind = a__U41 a__isNatKind = a__plus a__U11 = a__U12 a__U11 = a__U21 a__U11 = a__U31 a__U11 = a__U41 a__U11 = a__plus a__U12 = a__U21 a__U12 = a__U31 a__U12 = a__U41 a__U12 = a__plus a__U21 = a__U31 a__U21 = a__U41 a__U21 = a__plus a__U31 = a__U41 a__U31 = a__plus a__U41 = a__plus ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0') -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0') -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0') -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0') -> c42 a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c:c1 tt :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c :: c2:c3 -> c17:c18:c19:c20 -> c:c1 A__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c2:c3 a__isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNAT :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c17:c18:c19:c20 c1 :: c:c1 c2 :: c4:c5 -> c17:c18:c19:c20 -> c2:c3 A__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c4:c5 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c6:c7 c6 :: c8:c9 -> c17:c18:c19:c20 -> c6:c7 A__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c10:c11 c10 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c10:c11 MARK :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c11 :: c10:c11 A__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c12:c13:c14 c12 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 A__PLUS :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c25:c26:c27 mark :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c13 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 c14 :: c12:c13:c14 A__AND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c15:c16 c15 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c15:c16 c16 :: c15:c16 0' :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c17 :: c17:c18:c19:c20 plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c18 :: c:c1 -> c15:c16 -> c21:c22:c23:c24 -> c17:c18:c19:c20 a__and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNATKIND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c21:c22:c23:c24 s :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c19 :: c6:c7 -> c21:c22:c23:c24 -> c17:c18:c19:c20 c20 :: c17:c18:c19:c20 c21 :: c21:c22:c23:c24 c22 :: c15:c16 -> c21:c22:c23:c24 -> c21:c22:c23:c24 c23 :: c21:c22:c23:c24 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 c25 :: c10:c11 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 c26 :: c12:c13:c14 -> c15:c16 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c27 :: c25:c26:c27 U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c28 :: c:c1 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c29 :: c2:c3 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c30 :: c17:c18:c19:c20 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c31 :: c4:c5 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c32 :: c6:c7 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c33 :: c8:c9 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c34 :: c10:c11 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c35 :: c12:c13:c14 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c36 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c37 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c38 :: c15:c16 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c39 :: c21:c22:c23:c24 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c40 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c41 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c42 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 a__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c:c11_43 :: c:c1 hole_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U412_43 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c2:c33_43 :: c2:c3 hole_c17:c18:c19:c204_43 :: c17:c18:c19:c20 hole_c4:c55_43 :: c4:c5 hole_c6:c76_43 :: c6:c7 hole_c8:c97_43 :: c8:c9 hole_c10:c118_43 :: c10:c11 hole_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c429_43 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 hole_c12:c13:c1410_43 :: c12:c13:c14 hole_c25:c26:c2711_43 :: c25:c26:c27 hole_c15:c1612_43 :: c15:c16 hole_c21:c22:c23:c2413_43 :: c21:c22:c23:c24 gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43 :: Nat -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43 :: Nat -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 gen_c21:c22:c23:c2416_43 :: Nat -> c21:c22:c23:c24 Generator Equations: gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0) <=> tt gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(x, 1)) <=> plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(x), tt) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(0) <=> c30(c17) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(+(x, 1)) <=> c28(c(c2(c4, c17), c17), gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(x)) gen_c21:c22:c23:c2416_43(0) <=> c21 gen_c21:c22:c23:c2416_43(+(x, 1)) <=> c22(c15(c30(c17)), gen_c21:c22:c23:c2416_43(x)) The following defined symbols remain to be analysed: a__U11, A__U11, A__U12, a__isNat, A__ISNAT, A__U21, A__U31, MARK, A__U41, A__PLUS, mark, A__AND, a__and, a__isNatKind, A__ISNATKIND, a__U12, a__U21, a__U31, a__U41, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 a__isNat < A__U11 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U31 A__U11 = MARK A__U11 = A__U41 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNATKIND a__isNat < A__U12 A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U31 A__U12 = MARK A__U12 = A__U41 A__U12 = A__PLUS A__U12 = A__AND A__U12 = A__ISNATKIND a__isNat < A__U21 a__isNat < A__PLUS a__isNat = mark a__isNat = a__and a__isNat = a__isNatKind a__isNat = a__U11 a__isNat = a__U12 a__isNat = a__U21 a__isNat = a__U31 a__isNat = a__U41 a__isNat = a__plus A__ISNAT = A__U21 A__ISNAT = A__U31 A__ISNAT = MARK A__ISNAT = A__U41 A__ISNAT = A__PLUS A__ISNAT = A__AND a__and < A__ISNAT a__isNatKind < A__ISNAT A__ISNAT = A__ISNATKIND A__U21 = A__U31 A__U21 = MARK A__U21 = A__U41 A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNATKIND A__U31 = MARK A__U31 = A__U41 A__U31 = A__PLUS A__U31 = A__AND A__U31 = A__ISNATKIND MARK = A__U41 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNATKIND A__U41 = A__PLUS mark < A__U41 A__U41 = A__AND A__U41 = A__ISNATKIND A__PLUS = A__AND a__and < A__PLUS A__PLUS = A__ISNATKIND mark = a__and mark = a__isNatKind mark = a__U11 mark = a__U12 mark = a__U21 mark = a__U31 mark = a__U41 mark = a__plus A__AND = A__ISNATKIND a__and = a__isNatKind a__and = a__U11 a__and = a__U12 a__and = a__U21 a__and = a__U31 a__and = a__U41 a__and = a__plus a__isNatKind < A__ISNATKIND a__isNatKind = a__U11 a__isNatKind = a__U12 a__isNatKind = a__U21 a__isNatKind = a__U31 a__isNatKind = a__U41 a__isNatKind = a__plus a__U11 = a__U12 a__U11 = a__U21 a__U11 = a__U31 a__U11 = a__U41 a__U11 = a__plus a__U12 = a__U21 a__U12 = a__U31 a__U12 = a__U41 a__U12 = a__plus a__U21 = a__U31 a__U21 = a__U41 a__U21 = a__plus a__U31 = a__U41 a__U31 = a__plus a__U41 = a__plus ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43)) -> gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43), rt in Omega(0) Induction Base: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(n5132111_43, 1))) ->_R^Omega(0) a__plus(mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43)), mark(tt)) ->_IH a__plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(c5132112_43), mark(tt)) ->_R^Omega(0) a__plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43), tt) ->_R^Omega(0) plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43), tt) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0') -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0') -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0') -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0') -> c42 a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c:c1 tt :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c :: c2:c3 -> c17:c18:c19:c20 -> c:c1 A__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c2:c3 a__isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNAT :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c17:c18:c19:c20 c1 :: c:c1 c2 :: c4:c5 -> c17:c18:c19:c20 -> c2:c3 A__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c4:c5 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c6:c7 c6 :: c8:c9 -> c17:c18:c19:c20 -> c6:c7 A__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c10:c11 c10 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c10:c11 MARK :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c11 :: c10:c11 A__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c12:c13:c14 c12 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 A__PLUS :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c25:c26:c27 mark :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c13 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 c14 :: c12:c13:c14 A__AND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c15:c16 c15 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c15:c16 c16 :: c15:c16 0' :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c17 :: c17:c18:c19:c20 plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c18 :: c:c1 -> c15:c16 -> c21:c22:c23:c24 -> c17:c18:c19:c20 a__and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNATKIND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c21:c22:c23:c24 s :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c19 :: c6:c7 -> c21:c22:c23:c24 -> c17:c18:c19:c20 c20 :: c17:c18:c19:c20 c21 :: c21:c22:c23:c24 c22 :: c15:c16 -> c21:c22:c23:c24 -> c21:c22:c23:c24 c23 :: c21:c22:c23:c24 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 c25 :: c10:c11 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 c26 :: c12:c13:c14 -> c15:c16 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c27 :: c25:c26:c27 U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c28 :: c:c1 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c29 :: c2:c3 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c30 :: c17:c18:c19:c20 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c31 :: c4:c5 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c32 :: c6:c7 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c33 :: c8:c9 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c34 :: c10:c11 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c35 :: c12:c13:c14 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c36 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c37 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c38 :: c15:c16 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c39 :: c21:c22:c23:c24 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c40 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c41 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c42 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 a__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c:c11_43 :: c:c1 hole_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U412_43 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c2:c33_43 :: c2:c3 hole_c17:c18:c19:c204_43 :: c17:c18:c19:c20 hole_c4:c55_43 :: c4:c5 hole_c6:c76_43 :: c6:c7 hole_c8:c97_43 :: c8:c9 hole_c10:c118_43 :: c10:c11 hole_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c429_43 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 hole_c12:c13:c1410_43 :: c12:c13:c14 hole_c25:c26:c2711_43 :: c25:c26:c27 hole_c15:c1612_43 :: c15:c16 hole_c21:c22:c23:c2413_43 :: c21:c22:c23:c24 gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43 :: Nat -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43 :: Nat -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 gen_c21:c22:c23:c2416_43 :: Nat -> c21:c22:c23:c24 Lemmas: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43)) -> gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43), rt in Omega(0) Generator Equations: gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0) <=> tt gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(x, 1)) <=> plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(x), tt) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(0) <=> c30(c17) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(+(x, 1)) <=> c28(c(c2(c4, c17), c17), gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(x)) gen_c21:c22:c23:c2416_43(0) <=> c21 gen_c21:c22:c23:c2416_43(+(x, 1)) <=> c22(c15(c30(c17)), gen_c21:c22:c23:c2416_43(x)) The following defined symbols remain to be analysed: a__U21, A__U11, A__U12, a__isNat, A__ISNAT, A__U21, A__U31, MARK, A__U41, A__PLUS, A__AND, a__and, a__isNatKind, A__ISNATKIND, a__U11, a__U12, a__U31, a__U41, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 a__isNat < A__U11 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U31 A__U11 = MARK A__U11 = A__U41 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNATKIND a__isNat < A__U12 A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U31 A__U12 = MARK A__U12 = A__U41 A__U12 = A__PLUS A__U12 = A__AND A__U12 = A__ISNATKIND a__isNat < A__U21 a__isNat < A__PLUS a__isNat = mark a__isNat = a__and a__isNat = a__isNatKind a__isNat = a__U11 a__isNat = a__U12 a__isNat = a__U21 a__isNat = a__U31 a__isNat = a__U41 a__isNat = a__plus A__ISNAT = A__U21 A__ISNAT = A__U31 A__ISNAT = MARK A__ISNAT = A__U41 A__ISNAT = A__PLUS A__ISNAT = A__AND a__and < A__ISNAT a__isNatKind < A__ISNAT A__ISNAT = A__ISNATKIND A__U21 = A__U31 A__U21 = MARK A__U21 = A__U41 A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNATKIND A__U31 = MARK A__U31 = A__U41 A__U31 = A__PLUS A__U31 = A__AND A__U31 = A__ISNATKIND MARK = A__U41 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNATKIND A__U41 = A__PLUS mark < A__U41 A__U41 = A__AND A__U41 = A__ISNATKIND A__PLUS = A__AND a__and < A__PLUS A__PLUS = A__ISNATKIND mark = a__and mark = a__isNatKind mark = a__U11 mark = a__U12 mark = a__U21 mark = a__U31 mark = a__U41 mark = a__plus A__AND = A__ISNATKIND a__and = a__isNatKind a__and = a__U11 a__and = a__U12 a__and = a__U21 a__and = a__U31 a__and = a__U41 a__and = a__plus a__isNatKind < A__ISNATKIND a__isNatKind = a__U11 a__isNatKind = a__U12 a__isNatKind = a__U21 a__isNatKind = a__U31 a__isNatKind = a__U41 a__isNatKind = a__plus a__U11 = a__U12 a__U11 = a__U21 a__U11 = a__U31 a__U11 = a__U41 a__U11 = a__plus a__U12 = a__U21 a__U12 = a__U31 a__U12 = a__U41 a__U12 = a__plus a__U21 = a__U31 a__U21 = a__U41 a__U21 = a__plus a__U31 = a__U41 a__U31 = a__plus a__U41 = a__plus ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__isNatKind(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n6818335_43))) -> *17_43, rt in Omega(0) Induction Base: a__isNatKind(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, 0))) Induction Step: a__isNatKind(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, +(n6818335_43, 1)))) ->_R^Omega(0) a__and(a__isNatKind(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n6818335_43))), isNatKind(tt)) ->_IH a__and(*17_43, isNatKind(tt)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (18) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0') -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0') -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0') -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0') -> c42 a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c:c1 tt :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c :: c2:c3 -> c17:c18:c19:c20 -> c:c1 A__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c2:c3 a__isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNAT :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c17:c18:c19:c20 c1 :: c:c1 c2 :: c4:c5 -> c17:c18:c19:c20 -> c2:c3 A__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c4:c5 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c6:c7 c6 :: c8:c9 -> c17:c18:c19:c20 -> c6:c7 A__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c10:c11 c10 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c10:c11 MARK :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c11 :: c10:c11 A__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c12:c13:c14 c12 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 A__PLUS :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c25:c26:c27 mark :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c13 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 c14 :: c12:c13:c14 A__AND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c15:c16 c15 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c15:c16 c16 :: c15:c16 0' :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c17 :: c17:c18:c19:c20 plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c18 :: c:c1 -> c15:c16 -> c21:c22:c23:c24 -> c17:c18:c19:c20 a__and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNATKIND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c21:c22:c23:c24 s :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c19 :: c6:c7 -> c21:c22:c23:c24 -> c17:c18:c19:c20 c20 :: c17:c18:c19:c20 c21 :: c21:c22:c23:c24 c22 :: c15:c16 -> c21:c22:c23:c24 -> c21:c22:c23:c24 c23 :: c21:c22:c23:c24 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 c25 :: c10:c11 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 c26 :: c12:c13:c14 -> c15:c16 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c27 :: c25:c26:c27 U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c28 :: c:c1 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c29 :: c2:c3 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c30 :: c17:c18:c19:c20 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c31 :: c4:c5 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c32 :: c6:c7 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c33 :: c8:c9 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c34 :: c10:c11 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c35 :: c12:c13:c14 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c36 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c37 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c38 :: c15:c16 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c39 :: c21:c22:c23:c24 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c40 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c41 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c42 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 a__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c:c11_43 :: c:c1 hole_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U412_43 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c2:c33_43 :: c2:c3 hole_c17:c18:c19:c204_43 :: c17:c18:c19:c20 hole_c4:c55_43 :: c4:c5 hole_c6:c76_43 :: c6:c7 hole_c8:c97_43 :: c8:c9 hole_c10:c118_43 :: c10:c11 hole_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c429_43 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 hole_c12:c13:c1410_43 :: c12:c13:c14 hole_c25:c26:c2711_43 :: c25:c26:c27 hole_c15:c1612_43 :: c15:c16 hole_c21:c22:c23:c2413_43 :: c21:c22:c23:c24 gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43 :: Nat -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43 :: Nat -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 gen_c21:c22:c23:c2416_43 :: Nat -> c21:c22:c23:c24 Lemmas: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43)) -> gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n5132111_43), rt in Omega(0) a__isNatKind(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n6818335_43))) -> *17_43, rt in Omega(0) Generator Equations: gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0) <=> tt gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(x, 1)) <=> plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(x), tt) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(0) <=> c30(c17) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(+(x, 1)) <=> c28(c(c2(c4, c17), c17), gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(x)) gen_c21:c22:c23:c2416_43(0) <=> c21 gen_c21:c22:c23:c2416_43(+(x, 1)) <=> c22(c15(c30(c17)), gen_c21:c22:c23:c2416_43(x)) The following defined symbols remain to be analysed: a__U11, A__U11, A__U12, a__isNat, A__ISNAT, A__U21, A__U31, MARK, A__U41, A__PLUS, mark, A__AND, a__and, A__ISNATKIND, a__U12, a__U21, a__U31, a__U41, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 a__isNat < A__U11 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U31 A__U11 = MARK A__U11 = A__U41 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNATKIND a__isNat < A__U12 A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U31 A__U12 = MARK A__U12 = A__U41 A__U12 = A__PLUS A__U12 = A__AND A__U12 = A__ISNATKIND a__isNat < A__U21 a__isNat < A__PLUS a__isNat = mark a__isNat = a__and a__isNat = a__isNatKind a__isNat = a__U11 a__isNat = a__U12 a__isNat = a__U21 a__isNat = a__U31 a__isNat = a__U41 a__isNat = a__plus A__ISNAT = A__U21 A__ISNAT = A__U31 A__ISNAT = MARK A__ISNAT = A__U41 A__ISNAT = A__PLUS A__ISNAT = A__AND a__and < A__ISNAT a__isNatKind < A__ISNAT A__ISNAT = A__ISNATKIND A__U21 = A__U31 A__U21 = MARK A__U21 = A__U41 A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNATKIND A__U31 = MARK A__U31 = A__U41 A__U31 = A__PLUS A__U31 = A__AND A__U31 = A__ISNATKIND MARK = A__U41 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNATKIND A__U41 = A__PLUS mark < A__U41 A__U41 = A__AND A__U41 = A__ISNATKIND A__PLUS = A__AND a__and < A__PLUS A__PLUS = A__ISNATKIND mark = a__and mark = a__isNatKind mark = a__U11 mark = a__U12 mark = a__U21 mark = a__U31 mark = a__U41 mark = a__plus A__AND = A__ISNATKIND a__and = a__isNatKind a__and = a__U11 a__and = a__U12 a__and = a__U21 a__and = a__U31 a__and = a__U41 a__and = a__plus a__isNatKind < A__ISNATKIND a__isNatKind = a__U11 a__isNatKind = a__U12 a__isNatKind = a__U21 a__isNatKind = a__U31 a__isNatKind = a__U41 a__isNatKind = a__plus a__U11 = a__U12 a__U11 = a__U21 a__U11 = a__U31 a__U11 = a__U41 a__U11 = a__plus a__U12 = a__U21 a__U12 = a__U31 a__U12 = a__U41 a__U12 = a__plus a__U21 = a__U31 a__U21 = a__U41 a__U21 = a__plus a__U31 = a__U41 a__U31 = a__plus a__U41 = a__plus ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43)) -> gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43), rt in Omega(0) Induction Base: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(n6823800_43, 1))) ->_R^Omega(0) a__plus(mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43)), mark(tt)) ->_IH a__plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(c6823801_43), mark(tt)) ->_R^Omega(0) a__plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43), tt) ->_R^Omega(0) plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43), tt) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (20) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0') -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0') -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0') -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0') -> c42 a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c:c1 tt :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c :: c2:c3 -> c17:c18:c19:c20 -> c:c1 A__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c2:c3 a__isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNAT :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c17:c18:c19:c20 c1 :: c:c1 c2 :: c4:c5 -> c17:c18:c19:c20 -> c2:c3 A__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c4:c5 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c6:c7 c6 :: c8:c9 -> c17:c18:c19:c20 -> c6:c7 A__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c10:c11 c10 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c10:c11 MARK :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c11 :: c10:c11 A__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c12:c13:c14 c12 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 A__PLUS :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c25:c26:c27 mark :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c13 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 c14 :: c12:c13:c14 A__AND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c15:c16 c15 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c15:c16 c16 :: c15:c16 0' :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c17 :: c17:c18:c19:c20 plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c18 :: c:c1 -> c15:c16 -> c21:c22:c23:c24 -> c17:c18:c19:c20 a__and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNATKIND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c21:c22:c23:c24 s :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c19 :: c6:c7 -> c21:c22:c23:c24 -> c17:c18:c19:c20 c20 :: c17:c18:c19:c20 c21 :: c21:c22:c23:c24 c22 :: c15:c16 -> c21:c22:c23:c24 -> c21:c22:c23:c24 c23 :: c21:c22:c23:c24 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 c25 :: c10:c11 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 c26 :: c12:c13:c14 -> c15:c16 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c27 :: c25:c26:c27 U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c28 :: c:c1 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c29 :: c2:c3 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c30 :: c17:c18:c19:c20 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c31 :: c4:c5 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c32 :: c6:c7 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c33 :: c8:c9 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c34 :: c10:c11 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c35 :: c12:c13:c14 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c36 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c37 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c38 :: c15:c16 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c39 :: c21:c22:c23:c24 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c40 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c41 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c42 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 a__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c:c11_43 :: c:c1 hole_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U412_43 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c2:c33_43 :: c2:c3 hole_c17:c18:c19:c204_43 :: c17:c18:c19:c20 hole_c4:c55_43 :: c4:c5 hole_c6:c76_43 :: c6:c7 hole_c8:c97_43 :: c8:c9 hole_c10:c118_43 :: c10:c11 hole_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c429_43 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 hole_c12:c13:c1410_43 :: c12:c13:c14 hole_c25:c26:c2711_43 :: c25:c26:c27 hole_c15:c1612_43 :: c15:c16 hole_c21:c22:c23:c2413_43 :: c21:c22:c23:c24 gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43 :: Nat -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43 :: Nat -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 gen_c21:c22:c23:c2416_43 :: Nat -> c21:c22:c23:c24 Lemmas: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43)) -> gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43), rt in Omega(0) a__isNatKind(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n6818335_43))) -> *17_43, rt in Omega(0) Generator Equations: gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0) <=> tt gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(x, 1)) <=> plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(x), tt) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(0) <=> c30(c17) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(+(x, 1)) <=> c28(c(c2(c4, c17), c17), gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(x)) gen_c21:c22:c23:c2416_43(0) <=> c21 gen_c21:c22:c23:c2416_43(+(x, 1)) <=> c22(c15(c30(c17)), gen_c21:c22:c23:c2416_43(x)) The following defined symbols remain to be analysed: a__U21, A__U11, A__U12, A__ISNAT, A__U21, A__U31, MARK, A__U41, A__PLUS, A__AND, A__ISNATKIND, a__U31, a__U41, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 a__isNat < A__U11 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U31 A__U11 = MARK A__U11 = A__U41 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNATKIND a__isNat < A__U12 A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U31 A__U12 = MARK A__U12 = A__U41 A__U12 = A__PLUS A__U12 = A__AND A__U12 = A__ISNATKIND a__isNat < A__U21 a__isNat < A__PLUS a__isNat = mark a__isNat = a__and a__isNat = a__isNatKind a__isNat = a__U11 a__isNat = a__U12 a__isNat = a__U21 a__isNat = a__U31 a__isNat = a__U41 a__isNat = a__plus A__ISNAT = A__U21 A__ISNAT = A__U31 A__ISNAT = MARK A__ISNAT = A__U41 A__ISNAT = A__PLUS A__ISNAT = A__AND a__and < A__ISNAT a__isNatKind < A__ISNAT A__ISNAT = A__ISNATKIND A__U21 = A__U31 A__U21 = MARK A__U21 = A__U41 A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNATKIND A__U31 = MARK A__U31 = A__U41 A__U31 = A__PLUS A__U31 = A__AND A__U31 = A__ISNATKIND MARK = A__U41 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNATKIND A__U41 = A__PLUS mark < A__U41 A__U41 = A__AND A__U41 = A__ISNATKIND A__PLUS = A__AND a__and < A__PLUS A__PLUS = A__ISNATKIND mark = a__and mark = a__isNatKind mark = a__U11 mark = a__U12 mark = a__U21 mark = a__U31 mark = a__U41 mark = a__plus A__AND = A__ISNATKIND a__and = a__isNatKind a__and = a__U11 a__and = a__U12 a__and = a__U21 a__and = a__U31 a__and = a__U41 a__and = a__plus a__isNatKind < A__ISNATKIND a__isNatKind = a__U11 a__isNatKind = a__U12 a__isNatKind = a__U21 a__isNatKind = a__U31 a__isNatKind = a__U41 a__isNatKind = a__plus a__U11 = a__U12 a__U11 = a__U21 a__U11 = a__U31 a__U11 = a__U41 a__U11 = a__plus a__U12 = a__U21 a__U12 = a__U31 a__U12 = a__U41 a__U12 = a__plus a__U21 = a__U31 a__U21 = a__U41 a__U21 = a__plus a__U31 = a__U41 a__U31 = a__plus a__U41 = a__plus ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43))) -> *17_43, rt in Omega(n9253701_43) Induction Base: MARK(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, 0))) Induction Step: MARK(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, +(n9253701_43, 1)))) ->_R^Omega(1) c36(A__PLUS(mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43))), mark(tt)), MARK(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43)))) ->_L^Omega(0) c36(A__PLUS(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43)), mark(tt)), MARK(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43)))) ->_L^Omega(0) c36(A__PLUS(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43)), gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0)), MARK(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43)))) ->_R^Omega(1) c36(c27, MARK(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43)))) ->_IH c36(c27, *17_43) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0') -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0') -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0') -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0') -> c42 a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c:c1 tt :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c :: c2:c3 -> c17:c18:c19:c20 -> c:c1 A__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c2:c3 a__isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNAT :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c17:c18:c19:c20 c1 :: c:c1 c2 :: c4:c5 -> c17:c18:c19:c20 -> c2:c3 A__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c4:c5 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c6:c7 c6 :: c8:c9 -> c17:c18:c19:c20 -> c6:c7 A__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c10:c11 c10 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c10:c11 MARK :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c11 :: c10:c11 A__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c12:c13:c14 c12 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 A__PLUS :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c25:c26:c27 mark :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c13 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 c14 :: c12:c13:c14 A__AND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c15:c16 c15 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c15:c16 c16 :: c15:c16 0' :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c17 :: c17:c18:c19:c20 plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c18 :: c:c1 -> c15:c16 -> c21:c22:c23:c24 -> c17:c18:c19:c20 a__and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNATKIND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c21:c22:c23:c24 s :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c19 :: c6:c7 -> c21:c22:c23:c24 -> c17:c18:c19:c20 c20 :: c17:c18:c19:c20 c21 :: c21:c22:c23:c24 c22 :: c15:c16 -> c21:c22:c23:c24 -> c21:c22:c23:c24 c23 :: c21:c22:c23:c24 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 c25 :: c10:c11 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 c26 :: c12:c13:c14 -> c15:c16 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c27 :: c25:c26:c27 U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c28 :: c:c1 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c29 :: c2:c3 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c30 :: c17:c18:c19:c20 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c31 :: c4:c5 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c32 :: c6:c7 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c33 :: c8:c9 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c34 :: c10:c11 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c35 :: c12:c13:c14 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c36 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c37 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c38 :: c15:c16 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c39 :: c21:c22:c23:c24 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c40 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c41 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c42 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 a__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c:c11_43 :: c:c1 hole_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U412_43 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c2:c33_43 :: c2:c3 hole_c17:c18:c19:c204_43 :: c17:c18:c19:c20 hole_c4:c55_43 :: c4:c5 hole_c6:c76_43 :: c6:c7 hole_c8:c97_43 :: c8:c9 hole_c10:c118_43 :: c10:c11 hole_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c429_43 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 hole_c12:c13:c1410_43 :: c12:c13:c14 hole_c25:c26:c2711_43 :: c25:c26:c27 hole_c15:c1612_43 :: c15:c16 hole_c21:c22:c23:c2413_43 :: c21:c22:c23:c24 gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43 :: Nat -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43 :: Nat -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 gen_c21:c22:c23:c2416_43 :: Nat -> c21:c22:c23:c24 Lemmas: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43)) -> gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43), rt in Omega(0) a__isNatKind(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n6818335_43))) -> *17_43, rt in Omega(0) Generator Equations: gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0) <=> tt gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(x, 1)) <=> plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(x), tt) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(0) <=> c30(c17) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(+(x, 1)) <=> c28(c(c2(c4, c17), c17), gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(x)) gen_c21:c22:c23:c2416_43(0) <=> c21 gen_c21:c22:c23:c2416_43(+(x, 1)) <=> c22(c15(c30(c17)), gen_c21:c22:c23:c2416_43(x)) The following defined symbols remain to be analysed: MARK, A__U21, A__U31, A__U41, A__PLUS, A__ISNATKIND They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U31 A__U11 = MARK A__U11 = A__U41 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNATKIND A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U31 A__U12 = MARK A__U12 = A__U41 A__U12 = A__PLUS A__U12 = A__AND A__U12 = A__ISNATKIND A__ISNAT = A__U21 A__ISNAT = A__U31 A__ISNAT = MARK A__ISNAT = A__U41 A__ISNAT = A__PLUS A__ISNAT = A__AND A__ISNAT = A__ISNATKIND A__U21 = A__U31 A__U21 = MARK A__U21 = A__U41 A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNATKIND A__U31 = MARK A__U31 = A__U41 A__U31 = A__PLUS A__U31 = A__AND A__U31 = A__ISNATKIND MARK = A__U41 MARK = A__PLUS MARK = A__AND MARK = A__ISNATKIND A__U41 = A__PLUS A__U41 = A__AND A__U41 = A__ISNATKIND A__PLUS = A__AND A__PLUS = A__ISNATKIND A__AND = A__ISNATKIND ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0') -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0') -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0') -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0') -> c42 a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c:c1 tt :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c :: c2:c3 -> c17:c18:c19:c20 -> c:c1 A__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c2:c3 a__isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNAT :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c17:c18:c19:c20 c1 :: c:c1 c2 :: c4:c5 -> c17:c18:c19:c20 -> c2:c3 A__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c4:c5 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c6:c7 c6 :: c8:c9 -> c17:c18:c19:c20 -> c6:c7 A__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c10:c11 c10 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c10:c11 MARK :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c11 :: c10:c11 A__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c12:c13:c14 c12 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 A__PLUS :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c25:c26:c27 mark :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c13 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c12:c13:c14 c14 :: c12:c13:c14 A__AND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c15:c16 c15 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c15:c16 c16 :: c15:c16 0' :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c17 :: c17:c18:c19:c20 plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c18 :: c:c1 -> c15:c16 -> c21:c22:c23:c24 -> c17:c18:c19:c20 a__and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 A__ISNATKIND :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> c21:c22:c23:c24 s :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c19 :: c6:c7 -> c21:c22:c23:c24 -> c17:c18:c19:c20 c20 :: c17:c18:c19:c20 c21 :: c21:c22:c23:c24 c22 :: c15:c16 -> c21:c22:c23:c24 -> c21:c22:c23:c24 c23 :: c21:c22:c23:c24 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 c25 :: c10:c11 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 c26 :: c12:c13:c14 -> c15:c16 -> c15:c16 -> c17:c18:c19:c20 -> c25:c26:c27 and :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c27 :: c25:c26:c27 U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c28 :: c:c1 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c29 :: c2:c3 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c30 :: c17:c18:c19:c20 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c31 :: c4:c5 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c32 :: c6:c7 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c33 :: c8:c9 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c34 :: c10:c11 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 c35 :: c12:c13:c14 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c36 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c37 :: c25:c26:c27 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c38 :: c15:c16 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c39 :: c21:c22:c23:c24 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c40 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c41 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 c42 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 a__U11 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c:c11_43 :: c:c1 hole_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U412_43 :: tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 hole_c2:c33_43 :: c2:c3 hole_c17:c18:c19:c204_43 :: c17:c18:c19:c20 hole_c4:c55_43 :: c4:c5 hole_c6:c76_43 :: c6:c7 hole_c8:c97_43 :: c8:c9 hole_c10:c118_43 :: c10:c11 hole_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c429_43 :: c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 hole_c12:c13:c1410_43 :: c12:c13:c14 hole_c25:c26:c2711_43 :: c25:c26:c27 hole_c15:c1612_43 :: c15:c16 hole_c21:c22:c23:c2413_43 :: c21:c22:c23:c24 gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43 :: Nat -> tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U41 gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43 :: Nat -> c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c42 gen_c21:c22:c23:c2416_43 :: Nat -> c21:c22:c23:c24 Lemmas: mark(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43)) -> gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(n6823800_43), rt in Omega(0) a__isNatKind(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n6818335_43))) -> *17_43, rt in Omega(0) MARK(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(1, n9253701_43))) -> *17_43, rt in Omega(n9253701_43) Generator Equations: gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(0) <=> tt gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(+(x, 1)) <=> plus(gen_tt:0':plus:isNatKind:s:isNat:and:U11:U12:U13:U21:U22:U31:U4114_43(x), tt) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(0) <=> c30(c17) gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(+(x, 1)) <=> c28(c(c2(c4, c17), c17), gen_c28:c29:c30:c31:c32:c33:c34:c35:c36:c37:c38:c39:c40:c41:c4215_43(x)) gen_c21:c22:c23:c2416_43(0) <=> c21 gen_c21:c22:c23:c2416_43(+(x, 1)) <=> c22(c15(c30(c17)), gen_c21:c22:c23:c2416_43(x)) The following defined symbols remain to be analysed: A__U21, A__U11, A__U12, A__ISNAT, A__U31, A__U41, A__PLUS, A__AND, A__ISNATKIND They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U31 A__U11 = MARK A__U11 = A__U41 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNATKIND A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U31 A__U12 = MARK A__U12 = A__U41 A__U12 = A__PLUS A__U12 = A__AND A__U12 = A__ISNATKIND A__ISNAT = A__U21 A__ISNAT = A__U31 A__ISNAT = MARK A__ISNAT = A__U41 A__ISNAT = A__PLUS A__ISNAT = A__AND A__ISNAT = A__ISNATKIND A__U21 = A__U31 A__U21 = MARK A__U21 = A__U41 A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNATKIND A__U31 = MARK A__U31 = A__U41 A__U31 = A__PLUS A__U31 = A__AND A__U31 = A__ISNATKIND MARK = A__U41 MARK = A__PLUS MARK = A__AND MARK = A__ISNATKIND A__U41 = A__PLUS A__U41 = A__AND A__U41 = A__ISNATKIND A__PLUS = A__AND A__PLUS = A__ISNATKIND A__AND = A__ISNATKIND ---------------------------------------- (27) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (28) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1] a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1] a__U13(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1] a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(X)) -> a__U13(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (29) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (30) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1] a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1] a__U13(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1] a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(X)) -> a__U13(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (31) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__isNatKind_1 a__and_2 a__isNat_1 a__U22_1 a__U11_3 a__U41_3 a__U31_2 a__U12_2 a__U21_2 a__U13_1 a__plus_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (32) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1] a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1] a__U13(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1] a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(X)) -> a__U13(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (33) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (34) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, 0, V2) -> a__U12(tt, V2) [2] a__U11(tt, plus(V1', V2'), V2) -> a__U12(a__U11(a__and(a__isNatKind(V1'), isNatKind(V2')), V1', V2'), V2) [2] a__U11(tt, s(V1''), V2) -> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) [2] a__U11(tt, V1, V2) -> a__U12(isNat(V1), V2) [2] a__U12(tt, 0) -> a__U13(tt) [2] a__U12(tt, plus(V11, V2'')) -> a__U13(a__U11(a__and(a__isNatKind(V11), isNatKind(V2'')), V11, V2'')) [2] a__U12(tt, s(V12)) -> a__U13(a__U21(a__isNatKind(V12), V12)) [2] a__U12(tt, V2) -> a__U13(isNat(V2)) [2] a__U13(tt) -> tt [1] a__U21(tt, 0) -> a__U22(tt) [2] a__U21(tt, plus(V13, V21)) -> a__U22(a__U11(a__and(a__isNatKind(V13), isNatKind(V21)), V13, V21)) [2] a__U21(tt, s(V14)) -> a__U22(a__U21(a__isNatKind(V14), V14)) [2] a__U21(tt, V1) -> a__U22(isNat(V1)) [2] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(0, V2)) -> a__U11(a__and(tt, isNatKind(V2)), 0, V2) [2] a__isNat(plus(plus(V15, V22), V2)) -> a__U11(a__and(a__and(a__isNatKind(V15), isNatKind(V22)), isNatKind(V2)), plus(V15, V22), V2) [2] a__isNat(plus(s(V16), V2)) -> a__U11(a__and(a__isNatKind(V16), isNatKind(V2)), s(V16), V2) [2] a__isNat(plus(V1, V2)) -> a__U11(a__and(isNatKind(V1), isNatKind(V2)), V1, V2) [2] a__isNat(s(0)) -> a__U21(tt, 0) [2] a__isNat(s(plus(V17, V23))) -> a__U21(a__and(a__isNatKind(V17), isNatKind(V23)), plus(V17, V23)) [2] a__isNat(s(s(V18))) -> a__U21(a__isNatKind(V18), s(V18)) [2] a__isNat(s(V1)) -> a__U21(isNatKind(V1), V1) [2] a__isNatKind(0) -> tt [1] a__isNatKind(plus(0, V2)) -> a__and(tt, isNatKind(V2)) [2] a__isNatKind(plus(plus(V19, V24), V2)) -> a__and(a__and(a__isNatKind(V19), isNatKind(V24)), isNatKind(V2)) [2] a__isNatKind(plus(s(V110), V2)) -> a__and(a__isNatKind(V110), isNatKind(V2)) [2] a__isNatKind(plus(V1, V2)) -> a__and(isNatKind(V1), isNatKind(V2)) [2] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(0, 0) -> a__U31(a__and(tt, isNatKind(0)), 0) [2] a__plus(plus(V111, V25), 0) -> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), isNatKind(V25)), V111, V25), isNatKind(plus(V111, V25))), plus(V111, V25)) [2] a__plus(s(V112), 0) -> a__U31(a__and(a__U21(a__isNatKind(V112), V112), isNatKind(s(V112))), s(V112)) [2] a__plus(N, 0) -> a__U31(a__and(isNat(N), isNatKind(N)), N) [2] a__plus(N, s(0)) -> a__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(N), isNatKind(N))), 0, N) [2] a__plus(N, s(plus(V113, V26))) -> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), isNatKind(V26)), V113, V26), isNatKind(plus(V113, V26))), and(isNat(N), isNatKind(N))), plus(V113, V26), N) [2] a__plus(N, s(s(V114))) -> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), isNatKind(s(V114))), and(isNat(N), isNatKind(N))), s(V114), N) [2] a__plus(N, s(M)) -> a__U41(a__and(a__and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [2] mark(U11(U11(X1104, X2104, X333), X2, X3)) -> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) [2] mark(U11(U12(X1105, X2105), X2, X3)) -> a__U11(a__U12(mark(X1105), X2105), X2, X3) [2] mark(U11(isNat(X100), X2, X3)) -> a__U11(a__isNat(X100), X2, X3) [2] mark(U11(U13(X101), X2, X3)) -> a__U11(a__U13(mark(X101)), X2, X3) [2] mark(U11(U21(X1106, X2106), X2, X3)) -> a__U11(a__U21(mark(X1106), X2106), X2, X3) [2] mark(U11(U22(X102), X2, X3)) -> a__U11(a__U22(mark(X102)), X2, X3) [2] mark(U11(U31(X1107, X2107), X2, X3)) -> a__U11(a__U31(mark(X1107), X2107), X2, X3) [2] mark(U11(U41(X1108, X2108, X334), X2, X3)) -> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) [2] mark(U11(plus(X1109, X2109), X2, X3)) -> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) [2] mark(U11(and(X1110, X2110), X2, X3)) -> a__U11(a__and(mark(X1110), X2110), X2, X3) [2] mark(U11(isNatKind(X103), X2, X3)) -> a__U11(a__isNatKind(X103), X2, X3) [2] mark(U11(tt, X2, X3)) -> a__U11(tt, X2, X3) [2] mark(U11(s(X104), X2, X3)) -> a__U11(s(mark(X104)), X2, X3) [2] mark(U11(0, X2, X3)) -> a__U11(0, X2, X3) [2] mark(U12(U11(X1111, X2111, X335), X2)) -> a__U12(a__U11(mark(X1111), X2111, X335), X2) [2] mark(U12(U12(X1112, X2112), X2)) -> a__U12(a__U12(mark(X1112), X2112), X2) [2] mark(U12(isNat(X105), X2)) -> a__U12(a__isNat(X105), X2) [2] mark(U12(U13(X106), X2)) -> a__U12(a__U13(mark(X106)), X2) [2] mark(U12(U21(X1113, X2113), X2)) -> a__U12(a__U21(mark(X1113), X2113), X2) [2] mark(U12(U22(X107), X2)) -> a__U12(a__U22(mark(X107)), X2) [2] mark(U12(U31(X1114, X2114), X2)) -> a__U12(a__U31(mark(X1114), X2114), X2) [2] mark(U12(U41(X1115, X2115, X336), X2)) -> a__U12(a__U41(mark(X1115), X2115, X336), X2) [2] mark(U12(plus(X1116, X2116), X2)) -> a__U12(a__plus(mark(X1116), mark(X2116)), X2) [2] mark(U12(and(X1117, X2117), X2)) -> a__U12(a__and(mark(X1117), X2117), X2) [2] mark(U12(isNatKind(X108), X2)) -> a__U12(a__isNatKind(X108), X2) [2] mark(U12(tt, X2)) -> a__U12(tt, X2) [2] mark(U12(s(X109), X2)) -> a__U12(s(mark(X109)), X2) [2] mark(U12(0, X2)) -> a__U12(0, X2) [2] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(U11(X1118, X2118, X337))) -> a__U13(a__U11(mark(X1118), X2118, X337)) [2] mark(U13(U12(X1119, X2119))) -> a__U13(a__U12(mark(X1119), X2119)) [2] mark(U13(isNat(X200))) -> a__U13(a__isNat(X200)) [2] mark(U13(U13(X201))) -> a__U13(a__U13(mark(X201))) [2] mark(U13(U21(X1120, X2120))) -> a__U13(a__U21(mark(X1120), X2120)) [2] mark(U13(U22(X202))) -> a__U13(a__U22(mark(X202))) [2] mark(U13(U31(X1121, X2121))) -> a__U13(a__U31(mark(X1121), X2121)) [2] mark(U13(U41(X1122, X2122, X338))) -> a__U13(a__U41(mark(X1122), X2122, X338)) [2] mark(U13(plus(X1123, X2123))) -> a__U13(a__plus(mark(X1123), mark(X2123))) [2] mark(U13(and(X1124, X2124))) -> a__U13(a__and(mark(X1124), X2124)) [2] mark(U13(isNatKind(X203))) -> a__U13(a__isNatKind(X203)) [2] mark(U13(tt)) -> a__U13(tt) [2] mark(U13(s(X204))) -> a__U13(s(mark(X204))) [2] mark(U13(0)) -> a__U13(0) [2] mark(U21(U11(X1125, X2125, X339), X2)) -> a__U21(a__U11(mark(X1125), X2125, X339), X2) [2] mark(U21(U12(X1126, X2126), X2)) -> a__U21(a__U12(mark(X1126), X2126), X2) [2] mark(U21(isNat(X205), X2)) -> a__U21(a__isNat(X205), X2) [2] mark(U21(U13(X206), X2)) -> a__U21(a__U13(mark(X206)), X2) [2] mark(U21(U21(X1127, X2127), X2)) -> a__U21(a__U21(mark(X1127), X2127), X2) [2] mark(U21(U22(X207), X2)) -> a__U21(a__U22(mark(X207)), X2) [2] mark(U21(U31(X1128, X2128), X2)) -> a__U21(a__U31(mark(X1128), X2128), X2) [2] mark(U21(U41(X1129, X2129, X340), X2)) -> a__U21(a__U41(mark(X1129), X2129, X340), X2) [2] mark(U21(plus(X1130, X2130), X2)) -> a__U21(a__plus(mark(X1130), mark(X2130)), X2) [2] mark(U21(and(X1131, X2131), X2)) -> a__U21(a__and(mark(X1131), X2131), X2) [2] mark(U21(isNatKind(X208), X2)) -> a__U21(a__isNatKind(X208), X2) [2] mark(U21(tt, X2)) -> a__U21(tt, X2) [2] mark(U21(s(X209), X2)) -> a__U21(s(mark(X209)), X2) [2] mark(U21(0, X2)) -> a__U21(0, X2) [2] mark(U22(U11(X1132, X2132, X341))) -> a__U22(a__U11(mark(X1132), X2132, X341)) [2] mark(U22(U12(X1133, X2133))) -> a__U22(a__U12(mark(X1133), X2133)) [2] mark(U22(isNat(X300))) -> a__U22(a__isNat(X300)) [2] mark(U22(U13(X301))) -> a__U22(a__U13(mark(X301))) [2] mark(U22(U21(X1134, X2134))) -> a__U22(a__U21(mark(X1134), X2134)) [2] mark(U22(U22(X302))) -> a__U22(a__U22(mark(X302))) [2] mark(U22(U31(X1135, X2135))) -> a__U22(a__U31(mark(X1135), X2135)) [2] mark(U22(U41(X1136, X2136, X342))) -> a__U22(a__U41(mark(X1136), X2136, X342)) [2] mark(U22(plus(X1137, X2137))) -> a__U22(a__plus(mark(X1137), mark(X2137))) [2] mark(U22(and(X1138, X2138))) -> a__U22(a__and(mark(X1138), X2138)) [2] mark(U22(isNatKind(X303))) -> a__U22(a__isNatKind(X303)) [2] mark(U22(tt)) -> a__U22(tt) [2] mark(U22(s(X304))) -> a__U22(s(mark(X304))) [2] mark(U22(0)) -> a__U22(0) [2] mark(U31(U11(X1139, X2139, X343), X2)) -> a__U31(a__U11(mark(X1139), X2139, X343), X2) [2] mark(U31(U12(X1140, X2140), X2)) -> a__U31(a__U12(mark(X1140), X2140), X2) [2] mark(U31(isNat(X305), X2)) -> a__U31(a__isNat(X305), X2) [2] mark(U31(U13(X306), X2)) -> a__U31(a__U13(mark(X306)), X2) [2] mark(U31(U21(X1141, X2141), X2)) -> a__U31(a__U21(mark(X1141), X2141), X2) [2] mark(U31(U22(X307), X2)) -> a__U31(a__U22(mark(X307)), X2) [2] mark(U31(U31(X1142, X2142), X2)) -> a__U31(a__U31(mark(X1142), X2142), X2) [2] mark(U31(U41(X1143, X2143, X344), X2)) -> a__U31(a__U41(mark(X1143), X2143, X344), X2) [2] mark(U31(plus(X1144, X2144), X2)) -> a__U31(a__plus(mark(X1144), mark(X2144)), X2) [2] mark(U31(and(X1145, X2145), X2)) -> a__U31(a__and(mark(X1145), X2145), X2) [2] mark(U31(isNatKind(X308), X2)) -> a__U31(a__isNatKind(X308), X2) [2] mark(U31(tt, X2)) -> a__U31(tt, X2) [2] mark(U31(s(X309), X2)) -> a__U31(s(mark(X309)), X2) [2] mark(U31(0, X2)) -> a__U31(0, X2) [2] mark(U41(U11(X1146, X2146, X345), X2, X3)) -> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) [2] mark(U41(U12(X1147, X2147), X2, X3)) -> a__U41(a__U12(mark(X1147), X2147), X2, X3) [2] mark(U41(isNat(X346), X2, X3)) -> a__U41(a__isNat(X346), X2, X3) [2] mark(U41(U13(X347), X2, X3)) -> a__U41(a__U13(mark(X347)), X2, X3) [2] mark(U41(U21(X1148, X2148), X2, X3)) -> a__U41(a__U21(mark(X1148), X2148), X2, X3) [2] mark(U41(U22(X348), X2, X3)) -> a__U41(a__U22(mark(X348)), X2, X3) [2] mark(U41(U31(X1149, X2149), X2, X3)) -> a__U41(a__U31(mark(X1149), X2149), X2, X3) [2] mark(U41(U41(X1150, X2150, X349), X2, X3)) -> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) [2] mark(U41(plus(X1151, X2151), X2, X3)) -> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) [2] mark(U41(and(X1152, X2152), X2, X3)) -> a__U41(a__and(mark(X1152), X2152), X2, X3) [2] mark(U41(isNatKind(X350), X2, X3)) -> a__U41(a__isNatKind(X350), X2, X3) [2] mark(U41(tt, X2, X3)) -> a__U41(tt, X2, X3) [2] mark(U41(s(X351), X2, X3)) -> a__U41(s(mark(X351)), X2, X3) [2] mark(U41(0, X2, X3)) -> a__U41(0, X2, X3) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(U11(X1258, X2258, X3116), X2)) -> a__and(a__U11(mark(X1258), X2258, X3116), X2) [2] mark(and(U12(X1259, X2259), X2)) -> a__and(a__U12(mark(X1259), X2259), X2) [2] mark(and(isNat(X441), X2)) -> a__and(a__isNat(X441), X2) [2] mark(and(U13(X442), X2)) -> a__and(a__U13(mark(X442)), X2) [2] mark(and(U21(X1260, X2260), X2)) -> a__and(a__U21(mark(X1260), X2260), X2) [2] mark(and(U22(X443), X2)) -> a__and(a__U22(mark(X443)), X2) [2] mark(and(U31(X1261, X2261), X2)) -> a__and(a__U31(mark(X1261), X2261), X2) [2] mark(and(U41(X1262, X2262, X3117), X2)) -> a__and(a__U41(mark(X1262), X2262, X3117), X2) [2] mark(and(plus(X1263, X2263), X2)) -> a__and(a__plus(mark(X1263), mark(X2263)), X2) [2] mark(and(and(X1264, X2264), X2)) -> a__and(a__and(mark(X1264), X2264), X2) [2] mark(and(isNatKind(X444), X2)) -> a__and(a__isNatKind(X444), X2) [2] mark(and(tt, X2)) -> a__and(tt, X2) [2] mark(and(s(X445), X2)) -> a__and(s(mark(X445)), X2) [2] mark(and(0, X2)) -> a__and(0, X2) [2] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (35) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) :|: V1'' >= 0, z = 1, z' = 1 + V1'', V2 >= 0, z'' = V2 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), V2) :|: z = 1, z' = 1 + V1' + V2', V2 >= 0, z'' = V2, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(V12), V12)) :|: z = 1, V12 >= 0, z' = 1 + V12 a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U12(z, z') -{ 2 }-> a__U13(1) :|: z = 1, z' = 0 a__U12(z, z') -{ 2 }-> a__U13(1 + V2) :|: z' = V2, z = 1, V2 >= 0 a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V14), V14)) :|: V14 >= 0, z = 1, z' = 1 + V14 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21 a__U21(z, z') -{ 2 }-> a__U22(1) :|: z = 1, z' = 0 a__U21(z, z') -{ 2 }-> a__U22(1 + V1) :|: V1 >= 0, z = 1, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 1 :|: z = 1 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(V18), 1 + V18) :|: V18 >= 0, z = 1 + (1 + V18) a__isNat(z) -{ 2 }-> a__U21(a__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2 a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), 1 + (1 + V114)), 1 + (1 + N) + (1 + N)), 1 + V114, N) :|: V114 >= 0, z' = 1 + (1 + V114), z = N, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + N) + (1 + N)), 1 + V113 + V26, N) :|: z = N, z' = 1 + (1 + V113 + V26), N >= 0, V113 >= 0, V26 >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + N) + (1 + N)), 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + M, 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(V112), V112), 1 + (1 + V112)), 1 + V112) :|: z = 1 + V112, V112 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + N, 1 + N), N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0 mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2 mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0 mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0 mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0 mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0 mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0 mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 0 mark(z) -{ 2 }-> a__U31(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(1 + mark(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137) mark(z) -{ 2 }-> a__U22(a__isNatKind(X303)) :|: z = 1 + (1 + X303), X303 >= 0 mark(z) -{ 2 }-> a__U22(a__isNat(X300)) :|: X300 >= 0, z = 1 + (1 + X300) mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0 mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0 mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X302))) :|: X302 >= 0, z = 1 + (1 + X302) mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0 mark(z) -{ 2 }-> a__U22(a__U13(mark(X301))) :|: X301 >= 0, z = 1 + (1 + X301) mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__U22(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U22(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U22(1 + mark(X304)) :|: z = 1 + (1 + X304), X304 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0 mark(z) -{ 2 }-> a__U21(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123) mark(z) -{ 2 }-> a__U13(a__isNatKind(X203)) :|: z = 1 + (1 + X203), X203 >= 0 mark(z) -{ 2 }-> a__U13(a__isNat(X200)) :|: z = 1 + (1 + X200), X200 >= 0 mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0 mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0 mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0 mark(z) -{ 2 }-> a__U13(a__U22(mark(X202))) :|: X202 >= 0, z = 1 + (1 + X202) mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0 mark(z) -{ 2 }-> a__U13(a__U13(mark(X201))) :|: X201 >= 0, z = 1 + (1 + X201) mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0 mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U13(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U13(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U13(1 + mark(X204)) :|: z = 1 + (1 + X204), X204 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0 mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0 mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0 mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (37) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U22(z) -{ 1 }-> 1 :|: z = 1 ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) :|: V1'' >= 0, z = 1, z' = 1 + V1'', V2 >= 0, z'' = V2 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), V2) :|: z = 1, z' = 1 + V1' + V2', V2 >= 0, z'' = V2, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(V12), V12)) :|: z = 1, V12 >= 0, z' = 1 + V12 a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U12(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1 a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U12(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V14), V14)) :|: V14 >= 0, z = 1, z' = 1 + V14 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21 a__U21(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U21(z, z') -{ 3 }-> 1 :|: V1 >= 0, z = 1, z' = V1, 1 + V1 = 1 a__U21(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U21(z, z') -{ 3 }-> 1 + X :|: V1 >= 0, z = 1, z' = V1, X >= 0, 1 + V1 = X a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 1 :|: z = 1 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(V18), 1 + V18) :|: V18 >= 0, z = 1 + (1 + V18) a__isNat(z) -{ 2 }-> a__U21(a__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2 a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), 1 + (1 + V114)), 1 + (1 + N) + (1 + N)), 1 + V114, N) :|: V114 >= 0, z' = 1 + (1 + V114), z = N, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + N) + (1 + N)), 1 + V113 + V26, N) :|: z = N, z' = 1 + (1 + V113 + V26), N >= 0, V113 >= 0, V26 >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + N) + (1 + N)), 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + M, 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(V112), V112), 1 + (1 + V112)), 1 + V112) :|: z = 1 + V112, V112 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + N, 1 + N), N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0 mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2 mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0 mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0 mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0 mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0 mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0 mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 0 mark(z) -{ 2 }-> a__U31(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(1 + mark(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137) mark(z) -{ 2 }-> a__U22(a__isNatKind(X303)) :|: z = 1 + (1 + X303), X303 >= 0 mark(z) -{ 2 }-> a__U22(a__isNat(X300)) :|: X300 >= 0, z = 1 + (1 + X300) mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0 mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0 mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X302))) :|: X302 >= 0, z = 1 + (1 + X302) mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0 mark(z) -{ 2 }-> a__U22(a__U13(mark(X301))) :|: X301 >= 0, z = 1 + (1 + X301) mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X304)) :|: z = 1 + (1 + X304), X304 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0 mark(z) -{ 2 }-> a__U21(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123) mark(z) -{ 2 }-> a__U13(a__isNatKind(X203)) :|: z = 1 + (1 + X203), X203 >= 0 mark(z) -{ 2 }-> a__U13(a__isNat(X200)) :|: z = 1 + (1 + X200), X200 >= 0 mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0 mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0 mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0 mark(z) -{ 2 }-> a__U13(a__U22(mark(X202))) :|: X202 >= 0, z = 1 + (1 + X202) mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0 mark(z) -{ 2 }-> a__U13(a__U13(mark(X201))) :|: X201 >= 0, z = 1 + (1 + X201) mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0 mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U13(1 + mark(X204)) :|: z = 1 + (1 + X204), X204 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0 mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0 mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0 mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (39) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z' - 1 >= 0, z = 1, z'' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), z'') :|: z = 1, z' = 1 + V1' + V2', z'' >= 0, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, z'') :|: z = 1, z'' >= 0, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0 a__U11(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 1, z' - 1 >= 0 a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X a__U12(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + z :|: z >= 0 a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z' - 1 >= 0, z = 1 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21 a__U21(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U21(z, z') -{ 3 }-> 1 :|: z' >= 0, z = 1, 1 + z' = 1 a__U21(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U21(z, z') -{ 3 }-> 1 + X :|: z' >= 0, z = 1, X >= 0, 1 + z' = X a__U21(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U22(z) -{ 1 }-> 1 :|: z = 1 a__U22(z) -{ 1 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__and(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2 a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatKind(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2 a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__and(1, 1 + (z - 1)) :|: z - 1 >= 0 a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + z :|: z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(z' - 2), z' - 2), 1 + (1 + (z' - 2))), 1 + (1 + z) + (1 + z)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + z) + (1 + z)), 1 + V113 + V26, z) :|: z' = 1 + (1 + V113 + V26), z >= 0, V113 >= 0, V26 >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + z) + (1 + z)), 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + (z' - 1), 1 + (z' - 1)), 1 + (1 + z) + (1 + z)), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + z, 1 + z), z) :|: z' = 0, z >= 0 a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0 mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2 mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0 mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0 mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0 mark(z) -{ 2 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0 mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0 mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0 mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 0 mark(z) -{ 2 }-> a__U31(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U31(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U31(1 + mark(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137) mark(z) -{ 2 }-> a__U22(a__isNatKind(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U22(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0 mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0 mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0 mark(z) -{ 2 }-> a__U22(a__U13(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0 mark(z) -{ 2 }-> a__U21(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123) mark(z) -{ 2 }-> a__U13(a__isNatKind(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U13(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0 mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0 mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0 mark(z) -{ 2 }-> a__U13(a__U22(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0 mark(z) -{ 2 }-> a__U13(a__U13(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0 mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U13(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0 mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0 mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0 mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (41) 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 ---------------------------------------- (42) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1] a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1] a__U13(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1] a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U13(X)) -> a__U13(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U13(X) -> U13(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (43) 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 ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 1 }-> a__U12(a__isNat(V1), V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z') -{ 1 }-> a__U13(a__isNat(V2)) :|: z' = V2, z = 1, V2 >= 0 a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U13(z) -{ 1 }-> 1 :|: z = 1 a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 1 }-> a__U22(a__isNat(V1)) :|: V1 >= 0, z = 1, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 1 :|: z = 1 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 1 }-> a__U21(a__isNatKind(V1), V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> a__U11(a__and(a__isNatKind(V1), 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> a__and(a__isNatKind(V1), 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 1 }-> a__U41(a__and(a__and(a__isNat(M), 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 1 }-> a__U31(a__and(a__isNat(N), 1 + N), N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U22(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U13(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U12(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U11(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (45) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0) -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0) -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0) -> c42 S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U12(z0, z1) -> c3 A__U13(tt) -> c4 A__U13(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(MARK(z0)) A__U31(z0, z1) -> c11 A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U41(z0, z1, z2) -> c14 A__AND(tt, z0) -> c15(MARK(z0)) A__AND(z0, z1) -> c16 A__ISNAT(0) -> c17 A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c20 A__ISNATKIND(0) -> c21 A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c24 A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c27 MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(tt) -> c40 MARK(s(z0)) -> c41(MARK(z0)) MARK(0) -> c42 K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_2, A__U13_1, A__U21_2, A__U22_1, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c1, c2_2, c3, c4, c5, c6_2, c7, c8, c9, c10_1, c11, c12_2, c13_2, c14, c15_1, c16, c17, c18_3, c19_2, c20, c21, c22_2, c23_1, c24, c25_3, c26_4, c27, c28_2, c29_2, c30_1, c31_2, c32_2, c33_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c40, c41_1, c42 ---------------------------------------- (47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 17 trailing nodes: A__U41(z0, z1, z2) -> c14 A__ISNAT(0) -> c17 A__U21(z0, z1) -> c7 A__ISNATKIND(z0) -> c24 A__AND(z0, z1) -> c16 A__U22(tt) -> c8 A__U13(tt) -> c4 A__PLUS(z0, z1) -> c27 A__ISNAT(z0) -> c20 A__U22(z0) -> c9 MARK(tt) -> c40 A__U31(z0, z1) -> c11 A__U11(z0, z1, z2) -> c1 A__ISNATKIND(0) -> c21 MARK(0) -> c42 A__U13(z0) -> c5 A__U12(z0, z1) -> c3 ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_2, A__U21_2, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c2_2, c6_2, c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c31_2, c32_2, c33_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2 Compound Symbols: c_2, c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1 ---------------------------------------- (51) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (52) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) The (relative) TRS S consists of the following rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (53) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (54) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (55) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (56) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(MARK(z0)) [1] A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c15(MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) [1] A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c30(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) [1] MARK(s(z0)) -> c41(MARK(z0)) [1] A__U12(tt, z0) -> c2(A__ISNAT(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] MARK(U13(z0)) -> c31(MARK(z0)) [1] MARK(U22(z0)) -> c33(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0) -> a__U13(a__isNat(z0)) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U13(tt) -> tt [0] a__U13(z0) -> U13(z0) [0] a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> mark(z0) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) [0] a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1)) -> a__U12(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U13(z0)) -> a__U13(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (57) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (58) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(MARK(z0)) [1] A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c15(MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) [1] A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c30(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) [1] MARK(s(z0)) -> c41(MARK(z0)) [1] A__U12(tt, z0) -> c2(A__ISNAT(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] MARK(U13(z0)) -> c31(MARK(z0)) [1] MARK(U22(z0)) -> c33(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0) -> a__U13(a__isNat(z0)) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U13(tt) -> tt [0] a__U13(z0) -> U13(z0) [0] a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> mark(z0) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) [0] a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1)) -> a__U12(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U13(z0)) -> a__U13(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] The TRS has the following type information: A__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c tt :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c :: c2 -> c18:c19 -> c A__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c2 a__isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 A__ISNAT :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c18:c19 A__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c10 c10 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c10 MARK :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 A__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c12:c13 c12 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c12:c13 A__PLUS :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c25:c26 mark :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c13 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c12:c13 A__AND :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c15 c15 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c15 plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c18 :: c -> c15 -> c22:c23 -> c18:c19 a__and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 a__isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 A__ISNATKIND :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c22:c23 s :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c19 :: c6 -> c22:c23 -> c18:c19 A__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> c6 c22 :: c15 -> c22:c23 -> c22:c23 c23 :: c22:c23 -> c22:c23 0 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c25 :: c10 -> c15 -> c18:c19 -> c25:c26 c26 :: c12:c13 -> c15 -> c15 -> c18:c19 -> c25:c26 and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c28 :: c -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c29 :: c2 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c30 :: c18:c19 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c32 :: c6 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c34 :: c10 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c35 :: c12:c13 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c36 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c37 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c38 :: c15 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c39 :: c22:c23 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c41 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c2 :: c18:c19 -> c2 c6 :: c18:c19 -> c6 U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c31 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 c33 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 a__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 a__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 a__U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 a__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 a__U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 a__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 a__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 a__plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22 Rewrite Strategy: INNERMOST ---------------------------------------- (59) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__U11_3 A__U31_2 A__U41_3 A__AND_2 A__ISNAT_1 A__ISNATKIND_1 A__PLUS_2 MARK_1 A__U12_2 A__U21_2 (c) The following functions are completely defined: a__U11_3 a__U12_2 a__U13_1 a__U21_2 a__U22_1 a__U31_2 a__U41_3 a__and_2 a__isNat_1 a__isNatKind_1 a__plus_2 mark_1 Due to the following rules being added: a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U13(v0) -> null_a__U13 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__U11, null_a__U12, null_a__U13, null_a__U21, null_a__U22, null_a__U31, null_a__U41, null_a__and, null_a__isNat, null_a__isNatKind, null_a__plus, null_mark, const, const1, const2, const3, const4, const5, const6, const7, const8, const9 ---------------------------------------- (60) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(MARK(z0)) [1] A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c15(MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) [1] A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c30(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) [1] MARK(s(z0)) -> c41(MARK(z0)) [1] A__U12(tt, z0) -> c2(A__ISNAT(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] MARK(U13(z0)) -> c31(MARK(z0)) [1] MARK(U22(z0)) -> c33(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0) -> a__U13(a__isNat(z0)) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U13(tt) -> tt [0] a__U13(z0) -> U13(z0) [0] a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> mark(z0) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) [0] a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1)) -> a__U12(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U13(z0)) -> a__U13(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U13(v0) -> null_a__U13 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c tt :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c :: c2 -> c18:c19 -> c A__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c2 a__isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNAT :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c18:c19 A__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c10 c10 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c10 MARK :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 A__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c12:c13 c12 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c12:c13 A__PLUS :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c25:c26 mark :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c13 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c12:c13 A__AND :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c15 c15 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c15 plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c18 :: c -> c15 -> c22:c23 -> c18:c19 a__and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNATKIND :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c22:c23 s :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c19 :: c6 -> c22:c23 -> c18:c19 A__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c6 c22 :: c15 -> c22:c23 -> c22:c23 c23 :: c22:c23 -> c22:c23 0 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c25 :: c10 -> c15 -> c18:c19 -> c25:c26 c26 :: c12:c13 -> c15 -> c15 -> c18:c19 -> c25:c26 and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c28 :: c -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c29 :: c2 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c30 :: c18:c19 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c32 :: c6 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c34 :: c10 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c35 :: c12:c13 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c36 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c37 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c38 :: c15 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c39 :: c22:c23 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c41 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c2 :: c18:c19 -> c2 c6 :: c18:c19 -> c6 U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c31 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c33 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 a__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_mark :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark const :: c const1 :: c2 const2 :: c18:c19 const3 :: c10 const4 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 const5 :: c12:c13 const6 :: c25:c26 const7 :: c15 const8 :: c22:c23 const9 :: c6 Rewrite Strategy: INNERMOST ---------------------------------------- (61) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (62) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U11(tt, 0, z1) -> c(A__U12(tt, z1), A__ISNAT(0)) [1] A__U11(tt, plus(z0', z1'), z1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0'), isNatKind(z1')), z0', z1'), z1), A__ISNAT(plus(z0', z1'))) [1] A__U11(tt, s(z0''), z1) -> c(A__U12(a__U21(a__isNatKind(z0''), z0''), z1), A__ISNAT(s(z0''))) [1] A__U11(tt, z0, z1) -> c(A__U12(isNat(z0), z1), A__ISNAT(z0)) [1] A__U11(tt, z0, z1) -> c(A__U12(null_a__isNat, z1), A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(MARK(z0)) [1] A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c15(MARK(z0)) [1] A__ISNAT(plus(0, z1)) -> c18(A__U11(a__and(tt, isNatKind(z1)), 0, z1), A__AND(tt, isNatKind(z1)), A__ISNATKIND(0)) [1] A__ISNAT(plus(0, z1)) -> c18(A__U11(a__and(tt, isNatKind(z1)), 0, z1), A__AND(isNatKind(0), isNatKind(z1)), A__ISNATKIND(0)) [1] A__ISNAT(plus(0, z1)) -> c18(A__U11(a__and(tt, isNatKind(z1)), 0, z1), A__AND(null_a__isNatKind, isNatKind(z1)), A__ISNATKIND(0)) [1] A__ISNAT(plus(plus(z0385, z1224), z1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0385), isNatKind(z1224)), isNatKind(z1)), plus(z0385, z1224), z1), A__AND(a__and(a__isNatKind(z0385), isNatKind(z1224)), isNatKind(z1)), A__ISNATKIND(plus(z0385, z1224))) [1] A__ISNAT(plus(plus(z0385, z1224), z1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0385), isNatKind(z1224)), isNatKind(z1)), plus(z0385, z1224), z1), A__AND(isNatKind(plus(z0385, z1224)), isNatKind(z1)), A__ISNATKIND(plus(z0385, z1224))) [1] A__ISNAT(plus(plus(z0385, z1224), z1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0385), isNatKind(z1224)), isNatKind(z1)), plus(z0385, z1224), z1), A__AND(null_a__isNatKind, isNatKind(z1)), A__ISNATKIND(plus(z0385, z1224))) [1] A__ISNAT(plus(s(z0386), z1)) -> c18(A__U11(a__and(a__isNatKind(z0386), isNatKind(z1)), s(z0386), z1), A__AND(a__isNatKind(z0386), isNatKind(z1)), A__ISNATKIND(s(z0386))) [1] A__ISNAT(plus(s(z0386), z1)) -> c18(A__U11(a__and(a__isNatKind(z0386), isNatKind(z1)), s(z0386), z1), A__AND(isNatKind(s(z0386)), isNatKind(z1)), A__ISNATKIND(s(z0386))) [1] A__ISNAT(plus(s(z0386), z1)) -> c18(A__U11(a__and(a__isNatKind(z0386), isNatKind(z1)), s(z0386), z1), A__AND(null_a__isNatKind, isNatKind(z1)), A__ISNATKIND(s(z0386))) [1] A__ISNAT(plus(0, z1)) -> c18(A__U11(a__and(isNatKind(0), isNatKind(z1)), 0, z1), A__AND(tt, isNatKind(z1)), A__ISNATKIND(0)) [1] A__ISNAT(plus(plus(z0387, z1225), z1)) -> c18(A__U11(a__and(isNatKind(plus(z0387, z1225)), isNatKind(z1)), plus(z0387, z1225), z1), A__AND(a__and(a__isNatKind(z0387), isNatKind(z1225)), isNatKind(z1)), A__ISNATKIND(plus(z0387, z1225))) [1] A__ISNAT(plus(s(z0388), z1)) -> c18(A__U11(a__and(isNatKind(s(z0388)), isNatKind(z1)), s(z0388), z1), A__AND(a__isNatKind(z0388), isNatKind(z1)), A__ISNATKIND(s(z0388))) [1] A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNAT(plus(0, z1)) -> c18(A__U11(a__and(null_a__isNatKind, isNatKind(z1)), 0, z1), A__AND(tt, isNatKind(z1)), A__ISNATKIND(0)) [1] A__ISNAT(plus(plus(z0389, z1226), z1)) -> c18(A__U11(a__and(null_a__isNatKind, isNatKind(z1)), plus(z0389, z1226), z1), A__AND(a__and(a__isNatKind(z0389), isNatKind(z1226)), isNatKind(z1)), A__ISNATKIND(plus(z0389, z1226))) [1] A__ISNAT(plus(s(z0390), z1)) -> c18(A__U11(a__and(null_a__isNatKind, isNatKind(z1)), s(z0390), z1), A__AND(a__isNatKind(z0390), isNatKind(z1)), A__ISNATKIND(s(z0390))) [1] A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(null_a__isNatKind, isNatKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(null_a__isNatKind, isNatKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0)) [1] A__ISNAT(s(plus(z0391, z1227))) -> c19(A__U21(a__and(a__isNatKind(z0391), isNatKind(z1227)), plus(z0391, z1227)), A__ISNATKIND(plus(z0391, z1227))) [1] A__ISNAT(s(s(z0392))) -> c19(A__U21(a__isNatKind(z0392), s(z0392)), A__ISNATKIND(s(z0392))) [1] A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c19(A__U21(null_a__isNatKind, z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(0, z1)) -> c22(A__AND(tt, isNatKind(z1)), A__ISNATKIND(0)) [1] A__ISNATKIND(plus(plus(z0393, z1228), z1)) -> c22(A__AND(a__and(a__isNatKind(z0393), isNatKind(z1228)), isNatKind(z1)), A__ISNATKIND(plus(z0393, z1228))) [1] A__ISNATKIND(plus(s(z0394), z1)) -> c22(A__AND(a__isNatKind(z0394), isNatKind(z1)), A__ISNATKIND(s(z0394))) [1] A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(null_a__isNatKind, isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) [1] A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(tt, isNatKind(0)), A__ISNAT(0)) [1] A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(isNat(0), isNatKind(0)), A__ISNAT(0)) [1] A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(null_a__isNat, isNatKind(0)), A__ISNAT(0)) [1] A__PLUS(plus(z0395, z1229), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), isNatKind(z1229)), z0395, z1229), isNatKind(plus(z0395, z1229))), plus(z0395, z1229)), A__AND(a__U11(a__and(a__isNatKind(z0395), isNatKind(z1229)), z0395, z1229), isNatKind(plus(z0395, z1229))), A__ISNAT(plus(z0395, z1229))) [1] A__PLUS(plus(z0395, z1229), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), isNatKind(z1229)), z0395, z1229), isNatKind(plus(z0395, z1229))), plus(z0395, z1229)), A__AND(isNat(plus(z0395, z1229)), isNatKind(plus(z0395, z1229))), A__ISNAT(plus(z0395, z1229))) [1] A__PLUS(plus(z0395, z1229), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), isNatKind(z1229)), z0395, z1229), isNatKind(plus(z0395, z1229))), plus(z0395, z1229)), A__AND(null_a__isNat, isNatKind(plus(z0395, z1229))), A__ISNAT(plus(z0395, z1229))) [1] A__PLUS(s(z0396), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), isNatKind(s(z0396))), s(z0396)), A__AND(a__U21(a__isNatKind(z0396), z0396), isNatKind(s(z0396))), A__ISNAT(s(z0396))) [1] A__PLUS(s(z0396), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), isNatKind(s(z0396))), s(z0396)), A__AND(isNat(s(z0396)), isNatKind(s(z0396))), A__ISNAT(s(z0396))) [1] A__PLUS(s(z0396), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), isNatKind(s(z0396))), s(z0396)), A__AND(null_a__isNat, isNatKind(s(z0396))), A__ISNAT(s(z0396))) [1] A__PLUS(0, 0) -> c25(A__U31(a__and(isNat(0), isNatKind(0)), 0), A__AND(tt, isNatKind(0)), A__ISNAT(0)) [1] A__PLUS(plus(z0397, z1230), 0) -> c25(A__U31(a__and(isNat(plus(z0397, z1230)), isNatKind(plus(z0397, z1230))), plus(z0397, z1230)), A__AND(a__U11(a__and(a__isNatKind(z0397), isNatKind(z1230)), z0397, z1230), isNatKind(plus(z0397, z1230))), A__ISNAT(plus(z0397, z1230))) [1] A__PLUS(s(z0398), 0) -> c25(A__U31(a__and(isNat(s(z0398)), isNatKind(s(z0398))), s(z0398)), A__AND(a__U21(a__isNatKind(z0398), z0398), isNatKind(s(z0398))), A__ISNAT(s(z0398))) [1] A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(isNat(z0), isNatKind(z0)), A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(null_a__isNat, isNatKind(z0)), A__ISNAT(z0)) [1] A__PLUS(0, 0) -> c25(A__U31(a__and(null_a__isNat, isNatKind(0)), 0), A__AND(tt, isNatKind(0)), A__ISNAT(0)) [1] A__PLUS(plus(z0399, z1231), 0) -> c25(A__U31(a__and(null_a__isNat, isNatKind(plus(z0399, z1231))), plus(z0399, z1231)), A__AND(a__U11(a__and(a__isNatKind(z0399), isNatKind(z1231)), z0399, z1231), isNatKind(plus(z0399, z1231))), A__ISNAT(plus(z0399, z1231))) [1] A__PLUS(s(z0400), 0) -> c25(A__U31(a__and(null_a__isNat, isNatKind(s(z0400))), s(z0400)), A__AND(a__U21(a__isNatKind(z0400), z0400), isNatKind(s(z0400))), A__ISNAT(s(z0400))) [1] A__PLUS(z0, 0) -> c25(A__U31(a__and(null_a__isNat, isNatKind(z0)), z0), A__AND(isNat(z0), isNatKind(z0)), A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c25(A__U31(a__and(null_a__isNat, isNatKind(z0)), z0), A__AND(null_a__isNat, isNatKind(z0)), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) [1] MARK(U11(U11(z0415, z1239, z263), z1, z2)) -> c28(A__U11(a__U11(mark(z0415), z1239, z263), z1, z2), MARK(U11(z0415, z1239, z263))) [1] MARK(U11(U12(z0416, z1240), z1, z2)) -> c28(A__U11(a__U12(mark(z0416), z1240), z1, z2), MARK(U12(z0416, z1240))) [1] MARK(U11(isNat(z0417), z1, z2)) -> c28(A__U11(a__isNat(z0417), z1, z2), MARK(isNat(z0417))) [1] MARK(U11(U13(z0418), z1, z2)) -> c28(A__U11(a__U13(mark(z0418)), z1, z2), MARK(U13(z0418))) [1] MARK(U11(U21(z0419, z1241), z1, z2)) -> c28(A__U11(a__U21(mark(z0419), z1241), z1, z2), MARK(U21(z0419, z1241))) [1] MARK(U11(U22(z0420), z1, z2)) -> c28(A__U11(a__U22(mark(z0420)), z1, z2), MARK(U22(z0420))) [1] MARK(U11(U31(z0421, z1242), z1, z2)) -> c28(A__U11(a__U31(mark(z0421), z1242), z1, z2), MARK(U31(z0421, z1242))) [1] MARK(U11(U41(z0422, z1243, z264), z1, z2)) -> c28(A__U11(a__U41(mark(z0422), z1243, z264), z1, z2), MARK(U41(z0422, z1243, z264))) [1] MARK(U11(plus(z0423, z1244), z1, z2)) -> c28(A__U11(a__plus(mark(z0423), mark(z1244)), z1, z2), MARK(plus(z0423, z1244))) [1] MARK(U11(and(z0424, z1245), z1, z2)) -> c28(A__U11(a__and(mark(z0424), z1245), z1, z2), MARK(and(z0424, z1245))) [1] MARK(U11(isNatKind(z0425), z1, z2)) -> c28(A__U11(a__isNatKind(z0425), z1, z2), MARK(isNatKind(z0425))) [1] MARK(U11(tt, z1, z2)) -> c28(A__U11(tt, z1, z2), MARK(tt)) [1] MARK(U11(s(z0426), z1, z2)) -> c28(A__U11(s(mark(z0426)), z1, z2), MARK(s(z0426))) [1] MARK(U11(0, z1, z2)) -> c28(A__U11(0, z1, z2), MARK(0)) [1] MARK(U11(z0, z1, z2)) -> c28(A__U11(null_mark, z1, z2), MARK(z0)) [1] MARK(U12(U11(z0427, z1246, z265), z1)) -> c29(A__U12(a__U11(mark(z0427), z1246, z265), z1), MARK(U11(z0427, z1246, z265))) [1] MARK(U12(U12(z0428, z1247), z1)) -> c29(A__U12(a__U12(mark(z0428), z1247), z1), MARK(U12(z0428, z1247))) [1] MARK(U12(isNat(z0429), z1)) -> c29(A__U12(a__isNat(z0429), z1), MARK(isNat(z0429))) [1] MARK(U12(U13(z0430), z1)) -> c29(A__U12(a__U13(mark(z0430)), z1), MARK(U13(z0430))) [1] MARK(U12(U21(z0431, z1248), z1)) -> c29(A__U12(a__U21(mark(z0431), z1248), z1), MARK(U21(z0431, z1248))) [1] MARK(U12(U22(z0432), z1)) -> c29(A__U12(a__U22(mark(z0432)), z1), MARK(U22(z0432))) [1] MARK(U12(U31(z0433, z1249), z1)) -> c29(A__U12(a__U31(mark(z0433), z1249), z1), MARK(U31(z0433, z1249))) [1] MARK(U12(U41(z0434, z1250, z266), z1)) -> c29(A__U12(a__U41(mark(z0434), z1250, z266), z1), MARK(U41(z0434, z1250, z266))) [1] MARK(U12(plus(z0435, z1251), z1)) -> c29(A__U12(a__plus(mark(z0435), mark(z1251)), z1), MARK(plus(z0435, z1251))) [1] MARK(U12(and(z0436, z1252), z1)) -> c29(A__U12(a__and(mark(z0436), z1252), z1), MARK(and(z0436, z1252))) [1] MARK(U12(isNatKind(z0437), z1)) -> c29(A__U12(a__isNatKind(z0437), z1), MARK(isNatKind(z0437))) [1] MARK(U12(tt, z1)) -> c29(A__U12(tt, z1), MARK(tt)) [1] MARK(U12(s(z0438), z1)) -> c29(A__U12(s(mark(z0438)), z1), MARK(s(z0438))) [1] MARK(U12(0, z1)) -> c29(A__U12(0, z1), MARK(0)) [1] MARK(U12(z0, z1)) -> c29(A__U12(null_mark, z1), MARK(z0)) [1] MARK(isNat(z0)) -> c30(A__ISNAT(z0)) [1] MARK(U21(U11(z0439, z1253, z267), z1)) -> c32(A__U21(a__U11(mark(z0439), z1253, z267), z1), MARK(U11(z0439, z1253, z267))) [1] MARK(U21(U12(z0440, z1254), z1)) -> c32(A__U21(a__U12(mark(z0440), z1254), z1), MARK(U12(z0440, z1254))) [1] MARK(U21(isNat(z0441), z1)) -> c32(A__U21(a__isNat(z0441), z1), MARK(isNat(z0441))) [1] MARK(U21(U13(z0442), z1)) -> c32(A__U21(a__U13(mark(z0442)), z1), MARK(U13(z0442))) [1] MARK(U21(U21(z0443, z1255), z1)) -> c32(A__U21(a__U21(mark(z0443), z1255), z1), MARK(U21(z0443, z1255))) [1] MARK(U21(U22(z0444), z1)) -> c32(A__U21(a__U22(mark(z0444)), z1), MARK(U22(z0444))) [1] MARK(U21(U31(z0445, z1256), z1)) -> c32(A__U21(a__U31(mark(z0445), z1256), z1), MARK(U31(z0445, z1256))) [1] MARK(U21(U41(z0446, z1257, z268), z1)) -> c32(A__U21(a__U41(mark(z0446), z1257, z268), z1), MARK(U41(z0446, z1257, z268))) [1] MARK(U21(plus(z0447, z1258), z1)) -> c32(A__U21(a__plus(mark(z0447), mark(z1258)), z1), MARK(plus(z0447, z1258))) [1] MARK(U21(and(z0448, z1259), z1)) -> c32(A__U21(a__and(mark(z0448), z1259), z1), MARK(and(z0448, z1259))) [1] MARK(U21(isNatKind(z0449), z1)) -> c32(A__U21(a__isNatKind(z0449), z1), MARK(isNatKind(z0449))) [1] MARK(U21(tt, z1)) -> c32(A__U21(tt, z1), MARK(tt)) [1] MARK(U21(s(z0450), z1)) -> c32(A__U21(s(mark(z0450)), z1), MARK(s(z0450))) [1] MARK(U21(0, z1)) -> c32(A__U21(0, z1), MARK(0)) [1] MARK(U21(z0, z1)) -> c32(A__U21(null_mark, z1), MARK(z0)) [1] MARK(U31(U11(z0451, z1260, z269), z1)) -> c34(A__U31(a__U11(mark(z0451), z1260, z269), z1), MARK(U11(z0451, z1260, z269))) [1] MARK(U31(U12(z0452, z1261), z1)) -> c34(A__U31(a__U12(mark(z0452), z1261), z1), MARK(U12(z0452, z1261))) [1] MARK(U31(isNat(z0453), z1)) -> c34(A__U31(a__isNat(z0453), z1), MARK(isNat(z0453))) [1] MARK(U31(U13(z0454), z1)) -> c34(A__U31(a__U13(mark(z0454)), z1), MARK(U13(z0454))) [1] MARK(U31(U21(z0455, z1262), z1)) -> c34(A__U31(a__U21(mark(z0455), z1262), z1), MARK(U21(z0455, z1262))) [1] MARK(U31(U22(z0456), z1)) -> c34(A__U31(a__U22(mark(z0456)), z1), MARK(U22(z0456))) [1] MARK(U31(U31(z0457, z1263), z1)) -> c34(A__U31(a__U31(mark(z0457), z1263), z1), MARK(U31(z0457, z1263))) [1] MARK(U31(U41(z0458, z1264, z270), z1)) -> c34(A__U31(a__U41(mark(z0458), z1264, z270), z1), MARK(U41(z0458, z1264, z270))) [1] MARK(U31(plus(z0459, z1265), z1)) -> c34(A__U31(a__plus(mark(z0459), mark(z1265)), z1), MARK(plus(z0459, z1265))) [1] MARK(U31(and(z0460, z1266), z1)) -> c34(A__U31(a__and(mark(z0460), z1266), z1), MARK(and(z0460, z1266))) [1] MARK(U31(isNatKind(z0461), z1)) -> c34(A__U31(a__isNatKind(z0461), z1), MARK(isNatKind(z0461))) [1] MARK(U31(tt, z1)) -> c34(A__U31(tt, z1), MARK(tt)) [1] MARK(U31(s(z0462), z1)) -> c34(A__U31(s(mark(z0462)), z1), MARK(s(z0462))) [1] MARK(U31(0, z1)) -> c34(A__U31(0, z1), MARK(0)) [1] MARK(U31(z0, z1)) -> c34(A__U31(null_mark, z1), MARK(z0)) [1] MARK(U41(U11(z0463, z1267, z271), z1, z2)) -> c35(A__U41(a__U11(mark(z0463), z1267, z271), z1, z2), MARK(U11(z0463, z1267, z271))) [1] MARK(U41(U12(z0464, z1268), z1, z2)) -> c35(A__U41(a__U12(mark(z0464), z1268), z1, z2), MARK(U12(z0464, z1268))) [1] MARK(U41(isNat(z0465), z1, z2)) -> c35(A__U41(a__isNat(z0465), z1, z2), MARK(isNat(z0465))) [1] MARK(U41(U13(z0466), z1, z2)) -> c35(A__U41(a__U13(mark(z0466)), z1, z2), MARK(U13(z0466))) [1] MARK(U41(U21(z0467, z1269), z1, z2)) -> c35(A__U41(a__U21(mark(z0467), z1269), z1, z2), MARK(U21(z0467, z1269))) [1] MARK(U41(U22(z0468), z1, z2)) -> c35(A__U41(a__U22(mark(z0468)), z1, z2), MARK(U22(z0468))) [1] MARK(U41(U31(z0469, z1270), z1, z2)) -> c35(A__U41(a__U31(mark(z0469), z1270), z1, z2), MARK(U31(z0469, z1270))) [1] MARK(U41(U41(z0470, z1271, z272), z1, z2)) -> c35(A__U41(a__U41(mark(z0470), z1271, z272), z1, z2), MARK(U41(z0470, z1271, z272))) [1] MARK(U41(plus(z0471, z1272), z1, z2)) -> c35(A__U41(a__plus(mark(z0471), mark(z1272)), z1, z2), MARK(plus(z0471, z1272))) [1] MARK(U41(and(z0472, z1273), z1, z2)) -> c35(A__U41(a__and(mark(z0472), z1273), z1, z2), MARK(and(z0472, z1273))) [1] MARK(U41(isNatKind(z0473), z1, z2)) -> c35(A__U41(a__isNatKind(z0473), z1, z2), MARK(isNatKind(z0473))) [1] MARK(U41(tt, z1, z2)) -> c35(A__U41(tt, z1, z2), MARK(tt)) [1] MARK(U41(s(z0474), z1, z2)) -> c35(A__U41(s(mark(z0474)), z1, z2), MARK(s(z0474))) [1] MARK(U41(0, z1, z2)) -> c35(A__U41(0, z1, z2), MARK(0)) [1] MARK(U41(z0, z1, z2)) -> c35(A__U41(null_mark, z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(U11(z0859, z1498, z2137), z1)) -> c38(A__AND(a__U11(mark(z0859), z1498, z2137), z1), MARK(U11(z0859, z1498, z2137))) [1] MARK(and(U12(z0860, z1499), z1)) -> c38(A__AND(a__U12(mark(z0860), z1499), z1), MARK(U12(z0860, z1499))) [1] MARK(and(isNat(z0861), z1)) -> c38(A__AND(a__isNat(z0861), z1), MARK(isNat(z0861))) [1] MARK(and(U13(z0862), z1)) -> c38(A__AND(a__U13(mark(z0862)), z1), MARK(U13(z0862))) [1] MARK(and(U21(z0863, z1500), z1)) -> c38(A__AND(a__U21(mark(z0863), z1500), z1), MARK(U21(z0863, z1500))) [1] MARK(and(U22(z0864), z1)) -> c38(A__AND(a__U22(mark(z0864)), z1), MARK(U22(z0864))) [1] MARK(and(U31(z0865, z1501), z1)) -> c38(A__AND(a__U31(mark(z0865), z1501), z1), MARK(U31(z0865, z1501))) [1] MARK(and(U41(z0866, z1502, z2138), z1)) -> c38(A__AND(a__U41(mark(z0866), z1502, z2138), z1), MARK(U41(z0866, z1502, z2138))) [1] MARK(and(plus(z0867, z1503), z1)) -> c38(A__AND(a__plus(mark(z0867), mark(z1503)), z1), MARK(plus(z0867, z1503))) [1] MARK(and(and(z0868, z1504), z1)) -> c38(A__AND(a__and(mark(z0868), z1504), z1), MARK(and(z0868, z1504))) [1] MARK(and(isNatKind(z0869), z1)) -> c38(A__AND(a__isNatKind(z0869), z1), MARK(isNatKind(z0869))) [1] MARK(and(tt, z1)) -> c38(A__AND(tt, z1), MARK(tt)) [1] MARK(and(s(z0870), z1)) -> c38(A__AND(s(mark(z0870)), z1), MARK(s(z0870))) [1] MARK(and(0, z1)) -> c38(A__AND(0, z1), MARK(0)) [1] MARK(and(z0, z1)) -> c38(A__AND(null_mark, z1), MARK(z0)) [1] MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) [1] MARK(s(z0)) -> c41(MARK(z0)) [1] A__U12(tt, z0) -> c2(A__ISNAT(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] MARK(U13(z0)) -> c31(MARK(z0)) [1] MARK(U22(z0)) -> c33(MARK(z0)) [1] a__U11(tt, 0, z1) -> a__U12(tt, z1) [0] a__U11(tt, plus(z0871, z1505), z1) -> a__U12(a__U11(a__and(a__isNatKind(z0871), isNatKind(z1505)), z0871, z1505), z1) [0] a__U11(tt, s(z0872), z1) -> a__U12(a__U21(a__isNatKind(z0872), z0872), z1) [0] a__U11(tt, z0, z1) -> a__U12(isNat(z0), z1) [0] a__U11(tt, z0, z1) -> a__U12(null_a__isNat, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, 0) -> a__U13(tt) [0] a__U12(tt, plus(z0873, z1506)) -> a__U13(a__U11(a__and(a__isNatKind(z0873), isNatKind(z1506)), z0873, z1506)) [0] a__U12(tt, s(z0874)) -> a__U13(a__U21(a__isNatKind(z0874), z0874)) [0] a__U12(tt, z0) -> a__U13(isNat(z0)) [0] a__U12(tt, z0) -> a__U13(null_a__isNat) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U13(tt) -> tt [0] a__U13(z0) -> U13(z0) [0] a__U21(tt, 0) -> a__U22(tt) [0] a__U21(tt, plus(z0875, z1507)) -> a__U22(a__U11(a__and(a__isNatKind(z0875), isNatKind(z1507)), z0875, z1507)) [0] a__U21(tt, s(z0876)) -> a__U22(a__U21(a__isNatKind(z0876), z0876)) [0] a__U21(tt, z0) -> a__U22(isNat(z0)) [0] a__U21(tt, z0) -> a__U22(null_a__isNat) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> mark(z0) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(plus(0, z1)) -> a__U11(a__and(tt, isNatKind(z1)), 0, z1) [0] a__isNat(plus(plus(z01069, z1620), z1)) -> a__U11(a__and(a__and(a__isNatKind(z01069), isNatKind(z1620)), isNatKind(z1)), plus(z01069, z1620), z1) [0] a__isNat(plus(s(z01070), z1)) -> a__U11(a__and(a__isNatKind(z01070), isNatKind(z1)), s(z01070), z1) [0] a__isNat(plus(z0, z1)) -> a__U11(a__and(isNatKind(z0), isNatKind(z1)), z0, z1) [0] a__isNat(plus(z0, z1)) -> a__U11(a__and(null_a__isNatKind, isNatKind(z1)), z0, z1) [0] a__isNat(s(0)) -> a__U21(tt, 0) [0] a__isNat(s(plus(z01071, z1621))) -> a__U21(a__and(a__isNatKind(z01071), isNatKind(z1621)), plus(z01071, z1621)) [0] a__isNat(s(s(z01072))) -> a__U21(a__isNatKind(z01072), s(z01072)) [0] a__isNat(s(z0)) -> a__U21(isNatKind(z0), z0) [0] a__isNat(s(z0)) -> a__U21(null_a__isNatKind, z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(0, z1)) -> a__and(tt, isNatKind(z1)) [0] a__isNatKind(plus(plus(z01073, z1622), z1)) -> a__and(a__and(a__isNatKind(z01073), isNatKind(z1622)), isNatKind(z1)) [0] a__isNatKind(plus(s(z01074), z1)) -> a__and(a__isNatKind(z01074), isNatKind(z1)) [0] a__isNatKind(plus(z0, z1)) -> a__and(isNatKind(z0), isNatKind(z1)) [0] a__isNatKind(plus(z0, z1)) -> a__and(null_a__isNatKind, isNatKind(z1)) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(0, 0) -> a__U31(a__and(tt, isNatKind(0)), 0) [0] a__plus(plus(z01075, z1623), 0) -> a__U31(a__and(a__U11(a__and(a__isNatKind(z01075), isNatKind(z1623)), z01075, z1623), isNatKind(plus(z01075, z1623))), plus(z01075, z1623)) [0] a__plus(s(z01076), 0) -> a__U31(a__and(a__U21(a__isNatKind(z01076), z01076), isNatKind(s(z01076))), s(z01076)) [0] a__plus(z0, 0) -> a__U31(a__and(isNat(z0), isNatKind(z0)), z0) [0] a__plus(z0, 0) -> a__U31(a__and(null_a__isNat, isNatKind(z0)), z0) [0] a__plus(z0, s(0)) -> a__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(z0), isNatKind(z0))), 0, z0) [0] a__plus(z0, s(plus(z01077, z1624))) -> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z01077), isNatKind(z1624)), z01077, z1624), isNatKind(plus(z01077, z1624))), and(isNat(z0), isNatKind(z0))), plus(z01077, z1624), z0) [0] a__plus(z0, s(s(z01078))) -> a__U41(a__and(a__and(a__U21(a__isNatKind(z01078), z01078), isNatKind(s(z01078))), and(isNat(z0), isNatKind(z0))), s(z01078), z0) [0] a__plus(z0, s(z1)) -> a__U41(a__and(a__and(isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) [0] a__plus(z0, s(z1)) -> a__U41(a__and(a__and(null_a__isNat, isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(U11(z01079, z1625, z2171), z1, z2)) -> a__U11(a__U11(mark(z01079), z1625, z2171), z1, z2) [0] mark(U11(U12(z01080, z1626), z1, z2)) -> a__U11(a__U12(mark(z01080), z1626), z1, z2) [0] mark(U11(isNat(z01081), z1, z2)) -> a__U11(a__isNat(z01081), z1, z2) [0] mark(U11(U13(z01082), z1, z2)) -> a__U11(a__U13(mark(z01082)), z1, z2) [0] mark(U11(U21(z01083, z1627), z1, z2)) -> a__U11(a__U21(mark(z01083), z1627), z1, z2) [0] mark(U11(U22(z01084), z1, z2)) -> a__U11(a__U22(mark(z01084)), z1, z2) [0] mark(U11(U31(z01085, z1628), z1, z2)) -> a__U11(a__U31(mark(z01085), z1628), z1, z2) [0] mark(U11(U41(z01086, z1629, z2172), z1, z2)) -> a__U11(a__U41(mark(z01086), z1629, z2172), z1, z2) [0] mark(U11(plus(z01087, z1630), z1, z2)) -> a__U11(a__plus(mark(z01087), mark(z1630)), z1, z2) [0] mark(U11(and(z01088, z1631), z1, z2)) -> a__U11(a__and(mark(z01088), z1631), z1, z2) [0] mark(U11(isNatKind(z01089), z1, z2)) -> a__U11(a__isNatKind(z01089), z1, z2) [0] mark(U11(tt, z1, z2)) -> a__U11(tt, z1, z2) [0] mark(U11(s(z01090), z1, z2)) -> a__U11(s(mark(z01090)), z1, z2) [0] mark(U11(0, z1, z2)) -> a__U11(0, z1, z2) [0] mark(U11(z0, z1, z2)) -> a__U11(null_mark, z1, z2) [0] mark(U12(U11(z01091, z1632, z2173), z1)) -> a__U12(a__U11(mark(z01091), z1632, z2173), z1) [0] mark(U12(U12(z01092, z1633), z1)) -> a__U12(a__U12(mark(z01092), z1633), z1) [0] mark(U12(isNat(z01093), z1)) -> a__U12(a__isNat(z01093), z1) [0] mark(U12(U13(z01094), z1)) -> a__U12(a__U13(mark(z01094)), z1) [0] mark(U12(U21(z01095, z1634), z1)) -> a__U12(a__U21(mark(z01095), z1634), z1) [0] mark(U12(U22(z01096), z1)) -> a__U12(a__U22(mark(z01096)), z1) [0] mark(U12(U31(z01097, z1635), z1)) -> a__U12(a__U31(mark(z01097), z1635), z1) [0] mark(U12(U41(z01098, z1636, z2174), z1)) -> a__U12(a__U41(mark(z01098), z1636, z2174), z1) [0] mark(U12(plus(z01099, z1637), z1)) -> a__U12(a__plus(mark(z01099), mark(z1637)), z1) [0] mark(U12(and(z01100, z1638), z1)) -> a__U12(a__and(mark(z01100), z1638), z1) [0] mark(U12(isNatKind(z01101), z1)) -> a__U12(a__isNatKind(z01101), z1) [0] mark(U12(tt, z1)) -> a__U12(tt, z1) [0] mark(U12(s(z01102), z1)) -> a__U12(s(mark(z01102)), z1) [0] mark(U12(0, z1)) -> a__U12(0, z1) [0] mark(U12(z0, z1)) -> a__U12(null_mark, z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U13(U11(z01103, z1639, z2175))) -> a__U13(a__U11(mark(z01103), z1639, z2175)) [0] mark(U13(U12(z01104, z1640))) -> a__U13(a__U12(mark(z01104), z1640)) [0] mark(U13(isNat(z01105))) -> a__U13(a__isNat(z01105)) [0] mark(U13(U13(z01106))) -> a__U13(a__U13(mark(z01106))) [0] mark(U13(U21(z01107, z1641))) -> a__U13(a__U21(mark(z01107), z1641)) [0] mark(U13(U22(z01108))) -> a__U13(a__U22(mark(z01108))) [0] mark(U13(U31(z01109, z1642))) -> a__U13(a__U31(mark(z01109), z1642)) [0] mark(U13(U41(z01110, z1643, z2176))) -> a__U13(a__U41(mark(z01110), z1643, z2176)) [0] mark(U13(plus(z01111, z1644))) -> a__U13(a__plus(mark(z01111), mark(z1644))) [0] mark(U13(and(z01112, z1645))) -> a__U13(a__and(mark(z01112), z1645)) [0] mark(U13(isNatKind(z01113))) -> a__U13(a__isNatKind(z01113)) [0] mark(U13(tt)) -> a__U13(tt) [0] mark(U13(s(z01114))) -> a__U13(s(mark(z01114))) [0] mark(U13(0)) -> a__U13(0) [0] mark(U13(z0)) -> a__U13(null_mark) [0] mark(U21(U11(z01115, z1646, z2177), z1)) -> a__U21(a__U11(mark(z01115), z1646, z2177), z1) [0] mark(U21(U12(z01116, z1647), z1)) -> a__U21(a__U12(mark(z01116), z1647), z1) [0] mark(U21(isNat(z01117), z1)) -> a__U21(a__isNat(z01117), z1) [0] mark(U21(U13(z01118), z1)) -> a__U21(a__U13(mark(z01118)), z1) [0] mark(U21(U21(z01119, z1648), z1)) -> a__U21(a__U21(mark(z01119), z1648), z1) [0] mark(U21(U22(z01120), z1)) -> a__U21(a__U22(mark(z01120)), z1) [0] mark(U21(U31(z01121, z1649), z1)) -> a__U21(a__U31(mark(z01121), z1649), z1) [0] mark(U21(U41(z01122, z1650, z2178), z1)) -> a__U21(a__U41(mark(z01122), z1650, z2178), z1) [0] mark(U21(plus(z01123, z1651), z1)) -> a__U21(a__plus(mark(z01123), mark(z1651)), z1) [0] mark(U21(and(z01124, z1652), z1)) -> a__U21(a__and(mark(z01124), z1652), z1) [0] mark(U21(isNatKind(z01125), z1)) -> a__U21(a__isNatKind(z01125), z1) [0] mark(U21(tt, z1)) -> a__U21(tt, z1) [0] mark(U21(s(z01126), z1)) -> a__U21(s(mark(z01126)), z1) [0] mark(U21(0, z1)) -> a__U21(0, z1) [0] mark(U21(z0, z1)) -> a__U21(null_mark, z1) [0] mark(U22(U11(z01127, z1653, z2179))) -> a__U22(a__U11(mark(z01127), z1653, z2179)) [0] mark(U22(U12(z01128, z1654))) -> a__U22(a__U12(mark(z01128), z1654)) [0] mark(U22(isNat(z01129))) -> a__U22(a__isNat(z01129)) [0] mark(U22(U13(z01130))) -> a__U22(a__U13(mark(z01130))) [0] mark(U22(U21(z01131, z1655))) -> a__U22(a__U21(mark(z01131), z1655)) [0] mark(U22(U22(z01132))) -> a__U22(a__U22(mark(z01132))) [0] mark(U22(U31(z01133, z1656))) -> a__U22(a__U31(mark(z01133), z1656)) [0] mark(U22(U41(z01134, z1657, z2180))) -> a__U22(a__U41(mark(z01134), z1657, z2180)) [0] mark(U22(plus(z01135, z1658))) -> a__U22(a__plus(mark(z01135), mark(z1658))) [0] mark(U22(and(z01136, z1659))) -> a__U22(a__and(mark(z01136), z1659)) [0] mark(U22(isNatKind(z01137))) -> a__U22(a__isNatKind(z01137)) [0] mark(U22(tt)) -> a__U22(tt) [0] mark(U22(s(z01138))) -> a__U22(s(mark(z01138))) [0] mark(U22(0)) -> a__U22(0) [0] mark(U22(z0)) -> a__U22(null_mark) [0] mark(U31(U11(z01139, z1660, z2181), z1)) -> a__U31(a__U11(mark(z01139), z1660, z2181), z1) [0] mark(U31(U12(z01140, z1661), z1)) -> a__U31(a__U12(mark(z01140), z1661), z1) [0] mark(U31(isNat(z01141), z1)) -> a__U31(a__isNat(z01141), z1) [0] mark(U31(U13(z01142), z1)) -> a__U31(a__U13(mark(z01142)), z1) [0] mark(U31(U21(z01143, z1662), z1)) -> a__U31(a__U21(mark(z01143), z1662), z1) [0] mark(U31(U22(z01144), z1)) -> a__U31(a__U22(mark(z01144)), z1) [0] mark(U31(U31(z01145, z1663), z1)) -> a__U31(a__U31(mark(z01145), z1663), z1) [0] mark(U31(U41(z01146, z1664, z2182), z1)) -> a__U31(a__U41(mark(z01146), z1664, z2182), z1) [0] mark(U31(plus(z01147, z1665), z1)) -> a__U31(a__plus(mark(z01147), mark(z1665)), z1) [0] mark(U31(and(z01148, z1666), z1)) -> a__U31(a__and(mark(z01148), z1666), z1) [0] mark(U31(isNatKind(z01149), z1)) -> a__U31(a__isNatKind(z01149), z1) [0] mark(U31(tt, z1)) -> a__U31(tt, z1) [0] mark(U31(s(z01150), z1)) -> a__U31(s(mark(z01150)), z1) [0] mark(U31(0, z1)) -> a__U31(0, z1) [0] mark(U31(z0, z1)) -> a__U31(null_mark, z1) [0] mark(U41(U11(z01151, z1667, z2183), z1, z2)) -> a__U41(a__U11(mark(z01151), z1667, z2183), z1, z2) [0] mark(U41(U12(z01152, z1668), z1, z2)) -> a__U41(a__U12(mark(z01152), z1668), z1, z2) [0] mark(U41(isNat(z01153), z1, z2)) -> a__U41(a__isNat(z01153), z1, z2) [0] mark(U41(U13(z01154), z1, z2)) -> a__U41(a__U13(mark(z01154)), z1, z2) [0] mark(U41(U21(z01155, z1669), z1, z2)) -> a__U41(a__U21(mark(z01155), z1669), z1, z2) [0] mark(U41(U22(z01156), z1, z2)) -> a__U41(a__U22(mark(z01156)), z1, z2) [0] mark(U41(U31(z01157, z1670), z1, z2)) -> a__U41(a__U31(mark(z01157), z1670), z1, z2) [0] mark(U41(U41(z01158, z1671, z2184), z1, z2)) -> a__U41(a__U41(mark(z01158), z1671, z2184), z1, z2) [0] mark(U41(plus(z01159, z1672), z1, z2)) -> a__U41(a__plus(mark(z01159), mark(z1672)), z1, z2) [0] mark(U41(and(z01160, z1673), z1, z2)) -> a__U41(a__and(mark(z01160), z1673), z1, z2) [0] mark(U41(isNatKind(z01161), z1, z2)) -> a__U41(a__isNatKind(z01161), z1, z2) [0] mark(U41(tt, z1, z2)) -> a__U41(tt, z1, z2) [0] mark(U41(s(z01162), z1, z2)) -> a__U41(s(mark(z01162)), z1, z2) [0] mark(U41(0, z1, z2)) -> a__U41(0, z1, z2) [0] mark(U41(z0, z1, z2)) -> a__U41(null_mark, z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(and(U11(z01355, z1786, z2217), z1)) -> a__and(a__U11(mark(z01355), z1786, z2217), z1) [0] mark(and(U12(z01356, z1787), z1)) -> a__and(a__U12(mark(z01356), z1787), z1) [0] mark(and(isNat(z01357), z1)) -> a__and(a__isNat(z01357), z1) [0] mark(and(U13(z01358), z1)) -> a__and(a__U13(mark(z01358)), z1) [0] mark(and(U21(z01359, z1788), z1)) -> a__and(a__U21(mark(z01359), z1788), z1) [0] mark(and(U22(z01360), z1)) -> a__and(a__U22(mark(z01360)), z1) [0] mark(and(U31(z01361, z1789), z1)) -> a__and(a__U31(mark(z01361), z1789), z1) [0] mark(and(U41(z01362, z1790, z2218), z1)) -> a__and(a__U41(mark(z01362), z1790, z2218), z1) [0] mark(and(plus(z01363, z1791), z1)) -> a__and(a__plus(mark(z01363), mark(z1791)), z1) [0] mark(and(and(z01364, z1792), z1)) -> a__and(a__and(mark(z01364), z1792), z1) [0] mark(and(isNatKind(z01365), z1)) -> a__and(a__isNatKind(z01365), z1) [0] mark(and(tt, z1)) -> a__and(tt, z1) [0] mark(and(s(z01366), z1)) -> a__and(s(mark(z01366)), z1) [0] mark(and(0, z1)) -> a__and(0, z1) [0] mark(and(z0, z1)) -> a__and(null_mark, z1) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U13(v0) -> null_a__U13 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c tt :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c :: c2 -> c18:c19 -> c A__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c2 a__isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNAT :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c18:c19 A__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c10 c10 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c10 MARK :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 A__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c12:c13 c12 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c12:c13 A__PLUS :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c25:c26 mark :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c13 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c12:c13 A__AND :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c15 c15 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c15 plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c18 :: c -> c15 -> c22:c23 -> c18:c19 a__and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNATKIND :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c22:c23 s :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c19 :: c6 -> c22:c23 -> c18:c19 A__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c6 c22 :: c15 -> c22:c23 -> c22:c23 c23 :: c22:c23 -> c22:c23 0 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c25 :: c10 -> c15 -> c18:c19 -> c25:c26 c26 :: c12:c13 -> c15 -> c15 -> c18:c19 -> c25:c26 and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c28 :: c -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c29 :: c2 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c30 :: c18:c19 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c32 :: c6 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c34 :: c10 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c35 :: c12:c13 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c36 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c37 :: c25:c26 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c38 :: c15 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c39 :: c22:c23 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c41 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 c2 :: c18:c19 -> c2 c6 :: c18:c19 -> c6 U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c31 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c33 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 a__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_mark :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark const :: c const1 :: c2 const2 :: c18:c19 const3 :: c10 const4 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33 const5 :: c12:c13 const6 :: c25:c26 const7 :: c15 const8 :: c22:c23 const9 :: c6 Rewrite Strategy: INNERMOST ---------------------------------------- (63) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__U13 => 0 null_a__U21 => 0 null_a__U22 => 0 null_a__U31 => 0 null_a__U41 => 0 null_a__and => 0 null_a__isNat => 0 null_a__isNatKind => 0 null_a__plus => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 const6 => 0 const7 => 0 const8 => 0 const9 => 0 ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0392), 1 + z0392) + A__ISNATKIND(1 + z0392) :|: z = 1 + (1 + z0392), z0392 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__and(a__isNatKind(z0391), 1 + z1227), 1 + z0391 + z1227) + A__ISNATKIND(1 + z0391 + z1227) :|: z = 1 + (1 + z0391 + z1227), z0391 >= 0, z1227 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(a__isNatKind(z0386), 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(1 + (1 + z0386), 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(1 + (1 + z0385 + z1224), 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + z1), 0, z1) + A__AND(1, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), 0, z1) + A__AND(1, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), 1 + z0390, z1) + A__AND(a__isNatKind(z0390), 1 + z1) + A__ISNATKIND(1 + z0390) :|: z1 >= 0, z = 1 + (1 + z0390) + z1, z0390 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), 1 + z0389 + z1226, z1) + A__AND(a__and(a__isNatKind(z0389), 1 + z1226), 1 + z1) + A__ISNATKIND(1 + z0389 + z1226) :|: z1226 >= 0, z1 >= 0, z = 1 + (1 + z0389 + z1226) + z1, z0389 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(1, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + (1 + z0388), 1 + z1), 1 + z0388, z1) + A__AND(a__isNatKind(z0388), 1 + z1) + A__ISNATKIND(1 + z0388) :|: z = 1 + (1 + z0388) + z1, z1 >= 0, z0388 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + (1 + z0387 + z1225), 1 + z1), 1 + z0387 + z1225, z1) + A__AND(a__and(a__isNatKind(z0387), 1 + z1225), 1 + z1) + A__ISNATKIND(1 + z0387 + z1225) :|: z1 >= 0, z = 1 + (1 + z0387 + z1225) + z1, z0387 >= 0, z1225 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0394), 1 + z1) + A__ISNATKIND(1 + z0394) :|: z1 >= 0, z = 1 + (1 + z0394) + z1, z0394 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(a__and(a__isNatKind(z0393), 1 + z1228), 1 + z1) + A__ISNATKIND(1 + z0393 + z1228) :|: z1 >= 0, z1228 >= 0, z = 1 + (1 + z0393 + z1228) + z1, z0393 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(1, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), 1 + (1 + z0396)), 1 + z0396) + A__AND(a__U21(a__isNatKind(z0396), z0396), 1 + (1 + z0396)) + A__ISNAT(1 + z0396) :|: z0396 >= 0, z = 1 + z0396, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), 1 + (1 + z0396)), 1 + z0396) + A__AND(0, 1 + (1 + z0396)) + A__ISNAT(1 + z0396) :|: z0396 >= 0, z = 1 + z0396, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), 1 + (1 + z0396)), 1 + z0396) + A__AND(1 + (1 + z0396), 1 + (1 + z0396)) + A__ISNAT(1 + z0396) :|: z0396 >= 0, z = 1 + z0396, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(0, 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(1 + (1 + z0395 + z1229), 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(0, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(1 + 0, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + z0), z0) + A__AND(0, 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + z0), z0) + A__AND(1 + z0, 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + (1 + z0400)), 1 + z0400) + A__AND(a__U21(a__isNatKind(z0400), z0400), 1 + (1 + z0400)) + A__ISNAT(1 + z0400) :|: z0400 >= 0, z = 1 + z0400, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + (1 + z0399 + z1231)), 1 + z0399 + z1231) + A__AND(a__U11(a__and(a__isNatKind(z0399), 1 + z1231), z0399, z1231), 1 + (1 + z0399 + z1231)) + A__ISNAT(1 + z0399 + z1231) :|: z = 1 + z0399 + z1231, z1231 >= 0, z0399 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + z0, 1 + z0), z0) + A__AND(0, 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + z0, 1 + z0), z0) + A__AND(1 + z0, 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + 0, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + (1 + z0398), 1 + (1 + z0398)), 1 + z0398) + A__AND(a__U21(a__isNatKind(z0398), z0398), 1 + (1 + z0398)) + A__ISNAT(1 + z0398) :|: z0398 >= 0, z = 1 + z0398, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + (1 + z0397 + z1230), 1 + (1 + z0397 + z1230)), 1 + z0397 + z1230) + A__AND(a__U11(a__and(a__isNatKind(z0397), 1 + z1230), z0397, z1230), 1 + (1 + z0397 + z1230)) + A__ISNAT(1 + z0397 + z1230) :|: z0397 >= 0, z = 1 + z0397 + z1230, z1230 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__and(a__and(a__isNat(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1, z0) + A__AND(a__and(a__isNat(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNat(z1), 1 + z1) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U21(a__isNatKind(z0''), z0''), z1) + A__ISNAT(1 + z0'') :|: z1 >= 0, z = 1, z' = 1 + z0'', z0'' >= 0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U11(a__and(a__isNatKind(z0'), 1 + z1'), z0', z1'), z1) + A__ISNAT(1 + z0' + z1') :|: z1 >= 0, z = 1, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1', z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U31(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__plus(mark(z0471), mark(z1272)), z1, z2) + MARK(1 + z0471 + z1272) :|: z0471 >= 0, z1 >= 0, z1272 >= 0, z = 1 + (1 + z0471 + z1272) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__isNatKind(z0473), z1, z2) + MARK(1 + z0473) :|: z1 >= 0, z = 1 + (1 + z0473) + z1 + z2, z0473 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__isNat(z0465), z1, z2) + MARK(1 + z0465) :|: z1 >= 0, z0465 >= 0, z = 1 + (1 + z0465) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__and(mark(z0472), z1273), z1, z2) + MARK(1 + z0472 + z1273) :|: z1 >= 0, z1273 >= 0, z2 >= 0, z = 1 + (1 + z0472 + z1273) + z1 + z2, z0472 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U41(mark(z0470), z1271, z272), z1, z2) + MARK(1 + z0470 + z1271 + z272) :|: z1271 >= 0, z1 >= 0, z0470 >= 0, z272 >= 0, z = 1 + (1 + z0470 + z1271 + z272) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U31(mark(z0469), z1270), z1, z2) + MARK(1 + z0469 + z1270) :|: z1 >= 0, z = 1 + (1 + z0469 + z1270) + z1 + z2, z0469 >= 0, z1270 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U22(mark(z0468)), z1, z2) + MARK(1 + z0468) :|: z = 1 + (1 + z0468) + z1 + z2, z1 >= 0, z0468 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U21(mark(z0467), z1269), z1, z2) + MARK(1 + z0467 + z1269) :|: z1 >= 0, z1269 >= 0, z0467 >= 0, z = 1 + (1 + z0467 + z1269) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U13(mark(z0466)), z1, z2) + MARK(1 + z0466) :|: z1 >= 0, z = 1 + (1 + z0466) + z1 + z2, z0466 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U12(mark(z0464), z1268), z1, z2) + MARK(1 + z0464 + z1268) :|: z1268 >= 0, z1 >= 0, z0464 >= 0, z = 1 + (1 + z0464 + z1268) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U11(mark(z0463), z1267, z271), z1, z2) + MARK(1 + z0463 + z1267 + z271) :|: z1 >= 0, z271 >= 0, z = 1 + (1 + z0463 + z1267 + z271) + z1 + z2, z0463 >= 0, z2 >= 0, z1267 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(1 + mark(z0474), z1, z2) + MARK(1 + z0474) :|: z1 >= 0, z0474 >= 0, z = 1 + (1 + z0474) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__plus(mark(z0459), mark(z1265)), z1) + MARK(1 + z0459 + z1265) :|: z1 >= 0, z1265 >= 0, z = 1 + (1 + z0459 + z1265) + z1, z0459 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__isNatKind(z0461), z1) + MARK(1 + z0461) :|: z1 >= 0, z = 1 + (1 + z0461) + z1, z0461 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__isNat(z0453), z1) + MARK(1 + z0453) :|: z1 >= 0, z = 1 + (1 + z0453) + z1, z0453 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__and(mark(z0460), z1266), z1) + MARK(1 + z0460 + z1266) :|: z1 >= 0, z0460 >= 0, z = 1 + (1 + z0460 + z1266) + z1, z1266 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U41(mark(z0458), z1264, z270), z1) + MARK(1 + z0458 + z1264 + z270) :|: z = 1 + (1 + z0458 + z1264 + z270) + z1, z1 >= 0, z0458 >= 0, z270 >= 0, z1264 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U31(mark(z0457), z1263), z1) + MARK(1 + z0457 + z1263) :|: z1 >= 0, z0457 >= 0, z1263 >= 0, z = 1 + (1 + z0457 + z1263) + z1 MARK(z) -{ 1 }-> 1 + A__U31(a__U22(mark(z0456)), z1) + MARK(1 + z0456) :|: z1 >= 0, z = 1 + (1 + z0456) + z1, z0456 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U21(mark(z0455), z1262), z1) + MARK(1 + z0455 + z1262) :|: z = 1 + (1 + z0455 + z1262) + z1, z1 >= 0, z0455 >= 0, z1262 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U13(mark(z0454)), z1) + MARK(1 + z0454) :|: z = 1 + (1 + z0454) + z1, z1 >= 0, z0454 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U12(mark(z0452), z1261), z1) + MARK(1 + z0452 + z1261) :|: z = 1 + (1 + z0452 + z1261) + z1, z1261 >= 0, z1 >= 0, z0452 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U11(mark(z0451), z1260, z269), z1) + MARK(1 + z0451 + z1260 + z269) :|: z1 >= 0, z = 1 + (1 + z0451 + z1260 + z269) + z1, z269 >= 0, z0451 >= 0, z1260 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(1 + mark(z0462), z1) + MARK(1 + z0462) :|: z1 >= 0, z = 1 + (1 + z0462) + z1, z0462 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__plus(mark(z0447), mark(z1258)), z1) + MARK(1 + z0447 + z1258) :|: z0447 >= 0, z1258 >= 0, z1 >= 0, z = 1 + (1 + z0447 + z1258) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0449), z1) + MARK(1 + z0449) :|: z1 >= 0, z = 1 + (1 + z0449) + z1, z0449 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__isNat(z0441), z1) + MARK(1 + z0441) :|: z1 >= 0, z0441 >= 0, z = 1 + (1 + z0441) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__and(mark(z0448), z1259), z1) + MARK(1 + z0448 + z1259) :|: z = 1 + (1 + z0448 + z1259) + z1, z1 >= 0, z0448 >= 0, z1259 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U41(mark(z0446), z1257, z268), z1) + MARK(1 + z0446 + z1257 + z268) :|: z1 >= 0, z = 1 + (1 + z0446 + z1257 + z268) + z1, z268 >= 0, z0446 >= 0, z1257 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U31(mark(z0445), z1256), z1) + MARK(1 + z0445 + z1256) :|: z = 1 + (1 + z0445 + z1256) + z1, z1 >= 0, z0445 >= 0, z1256 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U22(mark(z0444)), z1) + MARK(1 + z0444) :|: z1 >= 0, z0444 >= 0, z = 1 + (1 + z0444) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z0443), z1255), z1) + MARK(1 + z0443 + z1255) :|: z = 1 + (1 + z0443 + z1255) + z1, z0443 >= 0, z1 >= 0, z1255 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U13(mark(z0442)), z1) + MARK(1 + z0442) :|: z1 >= 0, z = 1 + (1 + z0442) + z1, z0442 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U12(mark(z0440), z1254), z1) + MARK(1 + z0440 + z1254) :|: z1254 >= 0, z = 1 + (1 + z0440 + z1254) + z1, z1 >= 0, z0440 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z0439), z1253, z267), z1) + MARK(1 + z0439 + z1253 + z267) :|: z = 1 + (1 + z0439 + z1253 + z267) + z1, z1 >= 0, z1253 >= 0, z0439 >= 0, z267 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U21(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z0450), z1) + MARK(1 + z0450) :|: z1 >= 0, z0450 >= 0, z = 1 + (1 + z0450) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__plus(mark(z0435), mark(z1251)), z1) + MARK(1 + z0435 + z1251) :|: z1 >= 0, z0435 >= 0, z1251 >= 0, z = 1 + (1 + z0435 + z1251) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__isNatKind(z0437), z1) + MARK(1 + z0437) :|: z0437 >= 0, z1 >= 0, z = 1 + (1 + z0437) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__isNat(z0429), z1) + MARK(1 + z0429) :|: z = 1 + (1 + z0429) + z1, z1 >= 0, z0429 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__and(mark(z0436), z1252), z1) + MARK(1 + z0436 + z1252) :|: z1 >= 0, z0436 >= 0, z1252 >= 0, z = 1 + (1 + z0436 + z1252) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__U41(mark(z0434), z1250, z266), z1) + MARK(1 + z0434 + z1250 + z266) :|: z1250 >= 0, z1 >= 0, z = 1 + (1 + z0434 + z1250 + z266) + z1, z0434 >= 0, z266 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U31(mark(z0433), z1249), z1) + MARK(1 + z0433 + z1249) :|: z = 1 + (1 + z0433 + z1249) + z1, z0433 >= 0, z1 >= 0, z1249 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U22(mark(z0432)), z1) + MARK(1 + z0432) :|: z1 >= 0, z = 1 + (1 + z0432) + z1, z0432 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U21(mark(z0431), z1248), z1) + MARK(1 + z0431 + z1248) :|: z1 >= 0, z = 1 + (1 + z0431 + z1248) + z1, z0431 >= 0, z1248 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U13(mark(z0430)), z1) + MARK(1 + z0430) :|: z1 >= 0, z = 1 + (1 + z0430) + z1, z0430 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z0428), z1247), z1) + MARK(1 + z0428 + z1247) :|: z1 >= 0, z0428 >= 0, z = 1 + (1 + z0428 + z1247) + z1, z1247 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z0427), z1246, z265), z1) + MARK(1 + z0427 + z1246 + z265) :|: z1 >= 0, z0427 >= 0, z = 1 + (1 + z0427 + z1246 + z265) + z1, z1246 >= 0, z265 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z0438), z1) + MARK(1 + z0438) :|: z1 >= 0, z = 1 + (1 + z0438) + z1, z0438 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z0423), mark(z1244)), z1, z2) + MARK(1 + z0423 + z1244) :|: z = 1 + (1 + z0423 + z1244) + z1 + z2, z1 >= 0, z1244 >= 0, z0423 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__isNatKind(z0425), z1, z2) + MARK(1 + z0425) :|: z1 >= 0, z0425 >= 0, z = 1 + (1 + z0425) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__isNat(z0417), z1, z2) + MARK(1 + z0417) :|: z1 >= 0, z0417 >= 0, z = 1 + (1 + z0417) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__and(mark(z0424), z1245), z1, z2) + MARK(1 + z0424 + z1245) :|: z1 >= 0, z1245 >= 0, z = 1 + (1 + z0424 + z1245) + z1 + z2, z0424 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U41(mark(z0422), z1243, z264), z1, z2) + MARK(1 + z0422 + z1243 + z264) :|: z1 >= 0, z1243 >= 0, z = 1 + (1 + z0422 + z1243 + z264) + z1 + z2, z264 >= 0, z2 >= 0, z0422 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U31(mark(z0421), z1242), z1, z2) + MARK(1 + z0421 + z1242) :|: z1 >= 0, z1242 >= 0, z0421 >= 0, z2 >= 0, z = 1 + (1 + z0421 + z1242) + z1 + z2 MARK(z) -{ 1 }-> 1 + A__U11(a__U22(mark(z0420)), z1, z2) + MARK(1 + z0420) :|: z1 >= 0, z = 1 + (1 + z0420) + z1 + z2, z0420 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z0419), z1241), z1, z2) + MARK(1 + z0419 + z1241) :|: z1 >= 0, z = 1 + (1 + z0419 + z1241) + z1 + z2, z1241 >= 0, z0419 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U13(mark(z0418)), z1, z2) + MARK(1 + z0418) :|: z1 >= 0, z = 1 + (1 + z0418) + z1 + z2, z0418 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z0416), z1240), z1, z2) + MARK(1 + z0416 + z1240) :|: z1 >= 0, z0416 >= 0, z = 1 + (1 + z0416 + z1240) + z1 + z2, z1240 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z0415), z1239, z263), z1, z2) + MARK(1 + z0415 + z1239 + z263) :|: z = 1 + (1 + z0415 + z1239 + z263) + z1 + z2, z1 >= 0, z0415 >= 0, z1239 >= 0, z263 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z0426), z1, z2) + MARK(1 + z0426) :|: z1 >= 0, z0426 >= 0, z2 >= 0, z = 1 + (1 + z0426) + z1 + z2 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__plus(mark(z0867), mark(z1503)), z1) + MARK(1 + z0867 + z1503) :|: z1 >= 0, z0867 >= 0, z = 1 + (1 + z0867 + z1503) + z1, z1503 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0869), z1) + MARK(1 + z0869) :|: z1 >= 0, z0869 >= 0, z = 1 + (1 + z0869) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__isNat(z0861), z1) + MARK(1 + z0861) :|: z1 >= 0, z = 1 + (1 + z0861) + z1, z0861 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z0868), z1504), z1) + MARK(1 + z0868 + z1504) :|: z0868 >= 0, z1 >= 0, z = 1 + (1 + z0868 + z1504) + z1, z1504 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U41(mark(z0866), z1502, z2138), z1) + MARK(1 + z0866 + z1502 + z2138) :|: z1 >= 0, z1502 >= 0, z2138 >= 0, z0866 >= 0, z = 1 + (1 + z0866 + z1502 + z2138) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U31(mark(z0865), z1501), z1) + MARK(1 + z0865 + z1501) :|: z1 >= 0, z1501 >= 0, z = 1 + (1 + z0865 + z1501) + z1, z0865 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U22(mark(z0864)), z1) + MARK(1 + z0864) :|: z = 1 + (1 + z0864) + z1, z0864 >= 0, z1 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U21(mark(z0863), z1500), z1) + MARK(1 + z0863 + z1500) :|: z1 >= 0, z0863 >= 0, z1500 >= 0, z = 1 + (1 + z0863 + z1500) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U13(mark(z0862)), z1) + MARK(1 + z0862) :|: z1 >= 0, z0862 >= 0, z = 1 + (1 + z0862) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U12(mark(z0860), z1499), z1) + MARK(1 + z0860 + z1499) :|: z0860 >= 0, z1 >= 0, z = 1 + (1 + z0860 + z1499) + z1, z1499 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U11(mark(z0859), z1498, z2137), z1) + MARK(1 + z0859 + z1498 + z2137) :|: z1 >= 0, z2137 >= 0, z1498 >= 0, z = 1 + (1 + z0859 + z1498 + z2137) + z1, z0859 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z0870), z1) + MARK(1 + z0870) :|: z = 1 + (1 + z0870) + z1, z0870 >= 0, z1 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U21(a__isNatKind(z0872), z0872), z1) :|: z' = 1 + z0872, z1 >= 0, z = 1, z0872 >= 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U11(a__and(a__isNatKind(z0871), 1 + z1505), z0871, z1505), z1) :|: z1 >= 0, z = 1, z0871 >= 0, z' = 1 + z0871 + z1505, z1505 >= 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1 + z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U12(z, z') -{ 0 }-> a__U13(a__U21(a__isNatKind(z0874), z0874)) :|: z0874 >= 0, z = 1, z' = 1 + z0874 a__U12(z, z') -{ 0 }-> a__U13(a__U11(a__and(a__isNatKind(z0873), 1 + z1506), z0873, z1506)) :|: z1506 >= 0, z = 1, z' = 1 + z0873 + z1506, z0873 >= 0 a__U12(z, z') -{ 0 }-> a__U13(1) :|: z = 1, z' = 0 a__U12(z, z') -{ 0 }-> a__U13(0) :|: z = 1, z0 >= 0, z' = z0 a__U12(z, z') -{ 0 }-> a__U13(1 + z0) :|: z = 1, z0 >= 0, z' = z0 a__U12(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U12(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U13(z) -{ 0 }-> 1 :|: z = 1 a__U13(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U13(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z0876), z0876)) :|: z = 1, z' = 1 + z0876, z0876 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__and(a__isNatKind(z0875), 1 + z1507), z0875, z1507)) :|: z = 1, z1507 >= 0, z' = 1 + z0875 + z1507, z0875 >= 0 a__U21(z, z') -{ 0 }-> a__U22(1) :|: z = 1, z' = 0 a__U21(z, z') -{ 0 }-> a__U22(0) :|: z = 1, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> a__U22(1 + z0) :|: z = 1, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z) -{ 0 }-> 1 :|: z = 1 a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z01072), 1 + z01072) :|: z01072 >= 0, z = 1 + (1 + z01072) a__isNat(z) -{ 0 }-> a__U21(a__and(a__isNatKind(z01071), 1 + z1621), 1 + z01071 + z1621) :|: z = 1 + (1 + z01071 + z1621), z01071 >= 0, z1621 >= 0 a__isNat(z) -{ 0 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + z0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z01070), 1 + z1), 1 + z01070, z1) :|: z01070 >= 0, z = 1 + (1 + z01070) + z1, z1 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__and(a__isNatKind(z01069), 1 + z1620), 1 + z1), 1 + z01069 + z1620, z1) :|: z1 >= 0, z1620 >= 0, z01069 >= 0, z = 1 + (1 + z01069 + z1620) + z1 a__isNat(z) -{ 0 }-> a__U11(a__and(1, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNat(z) -{ 0 }-> a__U11(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__U11(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__and(a__isNatKind(z01074), 1 + z1) :|: z01074 >= 0, z1 >= 0, z = 1 + (1 + z01074) + z1 a__isNatKind(z) -{ 0 }-> a__and(a__and(a__isNatKind(z01073), 1 + z1622), 1 + z1) :|: z1622 >= 0, z1 >= 0, z01073 >= 0, z = 1 + (1 + z01073 + z1622) + z1 a__isNatKind(z) -{ 0 }-> a__and(1, 1 + z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(z01078), z01078), 1 + (1 + z01078)), 1 + (1 + z0) + (1 + z0)), 1 + z01078, z0) :|: z01078 >= 0, z = z0, z' = 1 + (1 + z01078), z0 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z01077), 1 + z1624), z01077, z1624), 1 + (1 + z01077 + z1624)), 1 + (1 + z0) + (1 + z0)), 1 + z01077 + z1624, z0) :|: z = z0, z1624 >= 0, z' = 1 + (1 + z01077 + z1624), z0 >= 0, z01077 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + z0) + (1 + z0)), 0, z0) :|: z = z0, z' = 1 + 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(0, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(1 + z1, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U31(a__and(a__U21(a__isNatKind(z01076), z01076), 1 + (1 + z01076)), 1 + z01076) :|: z = 1 + z01076, z01076 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(z01075), 1 + z1623), z01075, z1623), 1 + (1 + z01075 + z1623)), 1 + z01075 + z1623) :|: z01075 >= 0, z1623 >= 0, z = 1 + z01075 + z1623, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(0, 1 + z0), z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(1 + z0, 1 + z0), z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__and(a__plus(mark(z01363), mark(z1791)), z1) :|: z = 1 + (1 + z01363 + z1791) + z1, z1 >= 0, z01363 >= 0, z1791 >= 0 mark(z) -{ 0 }-> a__and(a__isNatKind(z01365), z1) :|: z = 1 + (1 + z01365) + z1, z1 >= 0, z01365 >= 0 mark(z) -{ 0 }-> a__and(a__isNat(z01357), z1) :|: z1 >= 0, z = 1 + (1 + z01357) + z1, z01357 >= 0 mark(z) -{ 0 }-> a__and(a__and(mark(z01364), z1792), z1) :|: z01364 >= 0, z1 >= 0, z = 1 + (1 + z01364 + z1792) + z1, z1792 >= 0 mark(z) -{ 0 }-> a__and(a__U41(mark(z01362), z1790, z2218), z1) :|: z2218 >= 0, z1790 >= 0, z1 >= 0, z = 1 + (1 + z01362 + z1790 + z2218) + z1, z01362 >= 0 mark(z) -{ 0 }-> a__and(a__U31(mark(z01361), z1789), z1) :|: z1 >= 0, z01361 >= 0, z = 1 + (1 + z01361 + z1789) + z1, z1789 >= 0 mark(z) -{ 0 }-> a__and(a__U22(mark(z01360)), z1) :|: z01360 >= 0, z1 >= 0, z = 1 + (1 + z01360) + z1 mark(z) -{ 0 }-> a__and(a__U21(mark(z01359), z1788), z1) :|: z1788 >= 0, z1 >= 0, z = 1 + (1 + z01359 + z1788) + z1, z01359 >= 0 mark(z) -{ 0 }-> a__and(a__U13(mark(z01358)), z1) :|: z1 >= 0, z01358 >= 0, z = 1 + (1 + z01358) + z1 mark(z) -{ 0 }-> a__and(a__U12(mark(z01356), z1787), z1) :|: z1 >= 0, z1787 >= 0, z = 1 + (1 + z01356 + z1787) + z1, z01356 >= 0 mark(z) -{ 0 }-> a__and(a__U11(mark(z01355), z1786, z2217), z1) :|: z1 >= 0, z2217 >= 0, z1786 >= 0, z01355 >= 0, z = 1 + (1 + z01355 + z1786 + z2217) + z1 mark(z) -{ 0 }-> a__and(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(1 + mark(z01366), z1) :|: z1 >= 0, z01366 >= 0, z = 1 + (1 + z01366) + z1 mark(z) -{ 0 }-> a__U41(a__plus(mark(z01159), mark(z1672)), z1, z2) :|: z1 >= 0, z01159 >= 0, z = 1 + (1 + z01159 + z1672) + z1 + z2, z1672 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__isNatKind(z01161), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01161) + z1 + z2, z01161 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__isNat(z01153), z1, z2) :|: z1 >= 0, z01153 >= 0, z = 1 + (1 + z01153) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__and(mark(z01160), z1673), z1, z2) :|: z = 1 + (1 + z01160 + z1673) + z1 + z2, z1 >= 0, z01160 >= 0, z1673 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U41(mark(z01158), z1671, z2184), z1, z2) :|: z1671 >= 0, z1 >= 0, z01158 >= 0, z = 1 + (1 + z01158 + z1671 + z2184) + z1 + z2, z2184 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U31(mark(z01157), z1670), z1, z2) :|: z1670 >= 0, z1 >= 0, z = 1 + (1 + z01157 + z1670) + z1 + z2, z01157 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U22(mark(z01156)), z1, z2) :|: z1 >= 0, z01156 >= 0, z2 >= 0, z = 1 + (1 + z01156) + z1 + z2 mark(z) -{ 0 }-> a__U41(a__U21(mark(z01155), z1669), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01155 + z1669) + z1 + z2, z1669 >= 0, z01155 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U13(mark(z01154)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01154) + z1 + z2, z01154 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U12(mark(z01152), z1668), z1, z2) :|: z1668 >= 0, z1 >= 0, z = 1 + (1 + z01152 + z1668) + z1 + z2, z01152 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U11(mark(z01151), z1667, z2183), z1, z2) :|: z1 >= 0, z1667 >= 0, z01151 >= 0, z = 1 + (1 + z01151 + z1667 + z2183) + z1 + z2, z2183 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(1 + mark(z01162), z1, z2) :|: z1 >= 0, z01162 >= 0, z = 1 + (1 + z01162) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U31(a__plus(mark(z01147), mark(z1665)), z1) :|: z = 1 + (1 + z01147 + z1665) + z1, z1 >= 0, z1665 >= 0, z01147 >= 0 mark(z) -{ 0 }-> a__U31(a__isNatKind(z01149), z1) :|: z01149 >= 0, z1 >= 0, z = 1 + (1 + z01149) + z1 mark(z) -{ 0 }-> a__U31(a__isNat(z01141), z1) :|: z = 1 + (1 + z01141) + z1, z01141 >= 0, z1 >= 0 mark(z) -{ 0 }-> a__U31(a__and(mark(z01148), z1666), z1) :|: z1 >= 0, z01148 >= 0, z1666 >= 0, z = 1 + (1 + z01148 + z1666) + z1 mark(z) -{ 0 }-> a__U31(a__U41(mark(z01146), z1664, z2182), z1) :|: z1664 >= 0, z1 >= 0, z = 1 + (1 + z01146 + z1664 + z2182) + z1, z2182 >= 0, z01146 >= 0 mark(z) -{ 0 }-> a__U31(a__U31(mark(z01145), z1663), z1) :|: z01145 >= 0, z1 >= 0, z = 1 + (1 + z01145 + z1663) + z1, z1663 >= 0 mark(z) -{ 0 }-> a__U31(a__U22(mark(z01144)), z1) :|: z1 >= 0, z01144 >= 0, z = 1 + (1 + z01144) + z1 mark(z) -{ 0 }-> a__U31(a__U21(mark(z01143), z1662), z1) :|: z1 >= 0, z1662 >= 0, z = 1 + (1 + z01143 + z1662) + z1, z01143 >= 0 mark(z) -{ 0 }-> a__U31(a__U13(mark(z01142)), z1) :|: z1 >= 0, z = 1 + (1 + z01142) + z1, z01142 >= 0 mark(z) -{ 0 }-> a__U31(a__U12(mark(z01140), z1661), z1) :|: z1 >= 0, z = 1 + (1 + z01140 + z1661) + z1, z01140 >= 0, z1661 >= 0 mark(z) -{ 0 }-> a__U31(a__U11(mark(z01139), z1660, z2181), z1) :|: z1660 >= 0, z2181 >= 0, z1 >= 0, z = 1 + (1 + z01139 + z1660 + z2181) + z1, z01139 >= 0 mark(z) -{ 0 }-> a__U31(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U31(1 + mark(z01150), z1) :|: z1 >= 0, z = 1 + (1 + z01150) + z1, z01150 >= 0 mark(z) -{ 0 }-> a__U22(a__plus(mark(z01135), mark(z1658))) :|: z01135 >= 0, z1658 >= 0, z = 1 + (1 + z01135 + z1658) mark(z) -{ 0 }-> a__U22(a__isNatKind(z01137)) :|: z = 1 + (1 + z01137), z01137 >= 0 mark(z) -{ 0 }-> a__U22(a__isNat(z01129)) :|: z01129 >= 0, z = 1 + (1 + z01129) mark(z) -{ 0 }-> a__U22(a__and(mark(z01136), z1659)) :|: z1659 >= 0, z = 1 + (1 + z01136 + z1659), z01136 >= 0 mark(z) -{ 0 }-> a__U22(a__U41(mark(z01134), z1657, z2180)) :|: z01134 >= 0, z1657 >= 0, z2180 >= 0, z = 1 + (1 + z01134 + z1657 + z2180) mark(z) -{ 0 }-> a__U22(a__U31(mark(z01133), z1656)) :|: z = 1 + (1 + z01133 + z1656), z1656 >= 0, z01133 >= 0 mark(z) -{ 0 }-> a__U22(a__U22(mark(z01132))) :|: z = 1 + (1 + z01132), z01132 >= 0 mark(z) -{ 0 }-> a__U22(a__U21(mark(z01131), z1655)) :|: z01131 >= 0, z = 1 + (1 + z01131 + z1655), z1655 >= 0 mark(z) -{ 0 }-> a__U22(a__U13(mark(z01130))) :|: z01130 >= 0, z = 1 + (1 + z01130) mark(z) -{ 0 }-> a__U22(a__U12(mark(z01128), z1654)) :|: z1654 >= 0, z01128 >= 0, z = 1 + (1 + z01128 + z1654) mark(z) -{ 0 }-> a__U22(a__U11(mark(z01127), z1653, z2179)) :|: z2179 >= 0, z01127 >= 0, z1653 >= 0, z = 1 + (1 + z01127 + z1653 + z2179) mark(z) -{ 0 }-> a__U22(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__U22(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__U22(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U22(1 + mark(z01138)) :|: z01138 >= 0, z = 1 + (1 + z01138) mark(z) -{ 0 }-> a__U21(a__plus(mark(z01123), mark(z1651)), z1) :|: z1 >= 0, z01123 >= 0, z1651 >= 0, z = 1 + (1 + z01123 + z1651) + z1 mark(z) -{ 0 }-> a__U21(a__isNatKind(z01125), z1) :|: z1 >= 0, z = 1 + (1 + z01125) + z1, z01125 >= 0 mark(z) -{ 0 }-> a__U21(a__isNat(z01117), z1) :|: z1 >= 0, z = 1 + (1 + z01117) + z1, z01117 >= 0 mark(z) -{ 0 }-> a__U21(a__and(mark(z01124), z1652), z1) :|: z1 >= 0, z01124 >= 0, z1652 >= 0, z = 1 + (1 + z01124 + z1652) + z1 mark(z) -{ 0 }-> a__U21(a__U41(mark(z01122), z1650, z2178), z1) :|: z2178 >= 0, z1650 >= 0, z1 >= 0, z01122 >= 0, z = 1 + (1 + z01122 + z1650 + z2178) + z1 mark(z) -{ 0 }-> a__U21(a__U31(mark(z01121), z1649), z1) :|: z1 >= 0, z01121 >= 0, z1649 >= 0, z = 1 + (1 + z01121 + z1649) + z1 mark(z) -{ 0 }-> a__U21(a__U22(mark(z01120)), z1) :|: z = 1 + (1 + z01120) + z1, z1 >= 0, z01120 >= 0 mark(z) -{ 0 }-> a__U21(a__U21(mark(z01119), z1648), z1) :|: z1 >= 0, z1648 >= 0, z01119 >= 0, z = 1 + (1 + z01119 + z1648) + z1 mark(z) -{ 0 }-> a__U21(a__U13(mark(z01118)), z1) :|: z = 1 + (1 + z01118) + z1, z1 >= 0, z01118 >= 0 mark(z) -{ 0 }-> a__U21(a__U12(mark(z01116), z1647), z1) :|: z1647 >= 0, z1 >= 0, z = 1 + (1 + z01116 + z1647) + z1, z01116 >= 0 mark(z) -{ 0 }-> a__U21(a__U11(mark(z01115), z1646, z2177), z1) :|: z1 >= 0, z1646 >= 0, z2177 >= 0, z = 1 + (1 + z01115 + z1646 + z2177) + z1, z01115 >= 0 mark(z) -{ 0 }-> a__U21(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U21(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U21(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U21(1 + mark(z01126), z1) :|: z1 >= 0, z = 1 + (1 + z01126) + z1, z01126 >= 0 mark(z) -{ 0 }-> a__U13(a__plus(mark(z01111), mark(z1644))) :|: z = 1 + (1 + z01111 + z1644), z01111 >= 0, z1644 >= 0 mark(z) -{ 0 }-> a__U13(a__isNatKind(z01113)) :|: z = 1 + (1 + z01113), z01113 >= 0 mark(z) -{ 0 }-> a__U13(a__isNat(z01105)) :|: z = 1 + (1 + z01105), z01105 >= 0 mark(z) -{ 0 }-> a__U13(a__and(mark(z01112), z1645)) :|: z01112 >= 0, z1645 >= 0, z = 1 + (1 + z01112 + z1645) mark(z) -{ 0 }-> a__U13(a__U41(mark(z01110), z1643, z2176)) :|: z1643 >= 0, z01110 >= 0, z = 1 + (1 + z01110 + z1643 + z2176), z2176 >= 0 mark(z) -{ 0 }-> a__U13(a__U31(mark(z01109), z1642)) :|: z = 1 + (1 + z01109 + z1642), z01109 >= 0, z1642 >= 0 mark(z) -{ 0 }-> a__U13(a__U22(mark(z01108))) :|: z = 1 + (1 + z01108), z01108 >= 0 mark(z) -{ 0 }-> a__U13(a__U21(mark(z01107), z1641)) :|: z = 1 + (1 + z01107 + z1641), z01107 >= 0, z1641 >= 0 mark(z) -{ 0 }-> a__U13(a__U13(mark(z01106))) :|: z = 1 + (1 + z01106), z01106 >= 0 mark(z) -{ 0 }-> a__U13(a__U12(mark(z01104), z1640)) :|: z01104 >= 0, z1640 >= 0, z = 1 + (1 + z01104 + z1640) mark(z) -{ 0 }-> a__U13(a__U11(mark(z01103), z1639, z2175)) :|: z01103 >= 0, z1639 >= 0, z2175 >= 0, z = 1 + (1 + z01103 + z1639 + z2175) mark(z) -{ 0 }-> a__U13(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__U13(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__U13(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U13(1 + mark(z01114)) :|: z01114 >= 0, z = 1 + (1 + z01114) mark(z) -{ 0 }-> a__U12(a__plus(mark(z01099), mark(z1637)), z1) :|: z01099 >= 0, z1 >= 0, z1637 >= 0, z = 1 + (1 + z01099 + z1637) + z1 mark(z) -{ 0 }-> a__U12(a__isNatKind(z01101), z1) :|: z1 >= 0, z = 1 + (1 + z01101) + z1, z01101 >= 0 mark(z) -{ 0 }-> a__U12(a__isNat(z01093), z1) :|: z1 >= 0, z = 1 + (1 + z01093) + z1, z01093 >= 0 mark(z) -{ 0 }-> a__U12(a__and(mark(z01100), z1638), z1) :|: z1 >= 0, z01100 >= 0, z1638 >= 0, z = 1 + (1 + z01100 + z1638) + z1 mark(z) -{ 0 }-> a__U12(a__U41(mark(z01098), z1636, z2174), z1) :|: z2174 >= 0, z01098 >= 0, z1 >= 0, z1636 >= 0, z = 1 + (1 + z01098 + z1636 + z2174) + z1 mark(z) -{ 0 }-> a__U12(a__U31(mark(z01097), z1635), z1) :|: z = 1 + (1 + z01097 + z1635) + z1, z1 >= 0, z1635 >= 0, z01097 >= 0 mark(z) -{ 0 }-> a__U12(a__U22(mark(z01096)), z1) :|: z = 1 + (1 + z01096) + z1, z1 >= 0, z01096 >= 0 mark(z) -{ 0 }-> a__U12(a__U21(mark(z01095), z1634), z1) :|: z1 >= 0, z01095 >= 0, z = 1 + (1 + z01095 + z1634) + z1, z1634 >= 0 mark(z) -{ 0 }-> a__U12(a__U13(mark(z01094)), z1) :|: z = 1 + (1 + z01094) + z1, z1 >= 0, z01094 >= 0 mark(z) -{ 0 }-> a__U12(a__U12(mark(z01092), z1633), z1) :|: z = 1 + (1 + z01092 + z1633) + z1, z1 >= 0, z01092 >= 0, z1633 >= 0 mark(z) -{ 0 }-> a__U12(a__U11(mark(z01091), z1632, z2173), z1) :|: z1 >= 0, z01091 >= 0, z = 1 + (1 + z01091 + z1632 + z2173) + z1, z2173 >= 0, z1632 >= 0 mark(z) -{ 0 }-> a__U12(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(1 + mark(z01102), z1) :|: z1 >= 0, z01102 >= 0, z = 1 + (1 + z01102) + z1 mark(z) -{ 0 }-> a__U11(a__plus(mark(z01087), mark(z1630)), z1, z2) :|: z1 >= 0, z1630 >= 0, z2 >= 0, z = 1 + (1 + z01087 + z1630) + z1 + z2, z01087 >= 0 mark(z) -{ 0 }-> a__U11(a__isNatKind(z01089), z1, z2) :|: z1 >= 0, z01089 >= 0, z = 1 + (1 + z01089) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__isNat(z01081), z1, z2) :|: z1 >= 0, z01081 >= 0, z2 >= 0, z = 1 + (1 + z01081) + z1 + z2 mark(z) -{ 0 }-> a__U11(a__and(mark(z01088), z1631), z1, z2) :|: z = 1 + (1 + z01088 + z1631) + z1 + z2, z01088 >= 0, z1 >= 0, z1631 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U41(mark(z01086), z1629, z2172), z1, z2) :|: z1 >= 0, z2172 >= 0, z01086 >= 0, z = 1 + (1 + z01086 + z1629 + z2172) + z1 + z2, z1629 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U31(mark(z01085), z1628), z1, z2) :|: z1 >= 0, z01085 >= 0, z1628 >= 0, z = 1 + (1 + z01085 + z1628) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U22(mark(z01084)), z1, z2) :|: z01084 >= 0, z1 >= 0, z = 1 + (1 + z01084) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U21(mark(z01083), z1627), z1, z2) :|: z1 >= 0, z1627 >= 0, z01083 >= 0, z = 1 + (1 + z01083 + z1627) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U13(mark(z01082)), z1, z2) :|: z1 >= 0, z01082 >= 0, z = 1 + (1 + z01082) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U12(mark(z01080), z1626), z1, z2) :|: z1626 >= 0, z01080 >= 0, z1 >= 0, z = 1 + (1 + z01080 + z1626) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z01079), z1625, z2171), z1, z2) :|: z = 1 + (1 + z01079 + z1625 + z2171) + z1 + z2, z1 >= 0, z1625 >= 0, z2171 >= 0, z01079 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1 + mark(z01090), z1, z2) :|: z = 1 + (1 + z01090) + z1 + z2, z1 >= 0, z01090 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (65) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__U13(z) -{ 0 }-> 1 :|: z = 1 a__U13(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U13(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U22(z) -{ 0 }-> 1 :|: z = 1 ---------------------------------------- (66) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0392), 1 + z0392) + A__ISNATKIND(1 + z0392) :|: z = 1 + (1 + z0392), z0392 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__and(a__isNatKind(z0391), 1 + z1227), 1 + z0391 + z1227) + A__ISNATKIND(1 + z0391 + z1227) :|: z = 1 + (1 + z0391 + z1227), z0391 >= 0, z1227 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(a__isNatKind(z0386), 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(1 + (1 + z0386), 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(1 + (1 + z0385 + z1224), 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + z1), 0, z1) + A__AND(1, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), 0, z1) + A__AND(1, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), 1 + z0390, z1) + A__AND(a__isNatKind(z0390), 1 + z1) + A__ISNATKIND(1 + z0390) :|: z1 >= 0, z = 1 + (1 + z0390) + z1, z0390 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), 1 + z0389 + z1226, z1) + A__AND(a__and(a__isNatKind(z0389), 1 + z1226), 1 + z1) + A__ISNATKIND(1 + z0389 + z1226) :|: z1226 >= 0, z1 >= 0, z = 1 + (1 + z0389 + z1226) + z1, z0389 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(1, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + (1 + z0388), 1 + z1), 1 + z0388, z1) + A__AND(a__isNatKind(z0388), 1 + z1) + A__ISNATKIND(1 + z0388) :|: z = 1 + (1 + z0388) + z1, z1 >= 0, z0388 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + (1 + z0387 + z1225), 1 + z1), 1 + z0387 + z1225, z1) + A__AND(a__and(a__isNatKind(z0387), 1 + z1225), 1 + z1) + A__ISNATKIND(1 + z0387 + z1225) :|: z1 >= 0, z = 1 + (1 + z0387 + z1225) + z1, z0387 >= 0, z1225 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0394), 1 + z1) + A__ISNATKIND(1 + z0394) :|: z1 >= 0, z = 1 + (1 + z0394) + z1, z0394 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(a__and(a__isNatKind(z0393), 1 + z1228), 1 + z1) + A__ISNATKIND(1 + z0393 + z1228) :|: z1 >= 0, z1228 >= 0, z = 1 + (1 + z0393 + z1228) + z1, z0393 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(1, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), 1 + (1 + z0396)), 1 + z0396) + A__AND(a__U21(a__isNatKind(z0396), z0396), 1 + (1 + z0396)) + A__ISNAT(1 + z0396) :|: z0396 >= 0, z = 1 + z0396, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), 1 + (1 + z0396)), 1 + z0396) + A__AND(0, 1 + (1 + z0396)) + A__ISNAT(1 + z0396) :|: z0396 >= 0, z = 1 + z0396, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z0396), z0396), 1 + (1 + z0396)), 1 + z0396) + A__AND(1 + (1 + z0396), 1 + (1 + z0396)) + A__ISNAT(1 + z0396) :|: z0396 >= 0, z = 1 + z0396, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(0, 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(1 + (1 + z0395 + z1229), 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(0, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(1 + 0, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + z0), z0) + A__AND(0, 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + z0), z0) + A__AND(1 + z0, 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + (1 + z0400)), 1 + z0400) + A__AND(a__U21(a__isNatKind(z0400), z0400), 1 + (1 + z0400)) + A__ISNAT(1 + z0400) :|: z0400 >= 0, z = 1 + z0400, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + (1 + z0399 + z1231)), 1 + z0399 + z1231) + A__AND(a__U11(a__and(a__isNatKind(z0399), 1 + z1231), z0399, z1231), 1 + (1 + z0399 + z1231)) + A__ISNAT(1 + z0399 + z1231) :|: z = 1 + z0399 + z1231, z1231 >= 0, z0399 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + z0, 1 + z0), z0) + A__AND(0, 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + z0, 1 + z0), z0) + A__AND(1 + z0, 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + 0, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + (1 + z0398), 1 + (1 + z0398)), 1 + z0398) + A__AND(a__U21(a__isNatKind(z0398), z0398), 1 + (1 + z0398)) + A__ISNAT(1 + z0398) :|: z0398 >= 0, z = 1 + z0398, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + (1 + z0397 + z1230), 1 + (1 + z0397 + z1230)), 1 + z0397 + z1230) + A__AND(a__U11(a__and(a__isNatKind(z0397), 1 + z1230), z0397, z1230), 1 + (1 + z0397 + z1230)) + A__ISNAT(1 + z0397 + z1230) :|: z0397 >= 0, z = 1 + z0397 + z1230, z1230 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__and(a__and(a__isNat(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1, z0) + A__AND(a__and(a__isNat(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNat(z1), 1 + z1) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U21(a__isNatKind(z0''), z0''), z1) + A__ISNAT(1 + z0'') :|: z1 >= 0, z = 1, z' = 1 + z0'', z0'' >= 0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U11(a__and(a__isNatKind(z0'), 1 + z1'), z0', z1'), z1) + A__ISNAT(1 + z0' + z1') :|: z1 >= 0, z = 1, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1', z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U31(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__plus(mark(z0471), mark(z1272)), z1, z2) + MARK(1 + z0471 + z1272) :|: z0471 >= 0, z1 >= 0, z1272 >= 0, z = 1 + (1 + z0471 + z1272) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__isNatKind(z0473), z1, z2) + MARK(1 + z0473) :|: z1 >= 0, z = 1 + (1 + z0473) + z1 + z2, z0473 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__isNat(z0465), z1, z2) + MARK(1 + z0465) :|: z1 >= 0, z0465 >= 0, z = 1 + (1 + z0465) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__and(mark(z0472), z1273), z1, z2) + MARK(1 + z0472 + z1273) :|: z1 >= 0, z1273 >= 0, z2 >= 0, z = 1 + (1 + z0472 + z1273) + z1 + z2, z0472 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U41(mark(z0470), z1271, z272), z1, z2) + MARK(1 + z0470 + z1271 + z272) :|: z1271 >= 0, z1 >= 0, z0470 >= 0, z272 >= 0, z = 1 + (1 + z0470 + z1271 + z272) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U31(mark(z0469), z1270), z1, z2) + MARK(1 + z0469 + z1270) :|: z1 >= 0, z = 1 + (1 + z0469 + z1270) + z1 + z2, z0469 >= 0, z1270 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U22(mark(z0468)), z1, z2) + MARK(1 + z0468) :|: z = 1 + (1 + z0468) + z1 + z2, z1 >= 0, z0468 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U21(mark(z0467), z1269), z1, z2) + MARK(1 + z0467 + z1269) :|: z1 >= 0, z1269 >= 0, z0467 >= 0, z = 1 + (1 + z0467 + z1269) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U13(mark(z0466)), z1, z2) + MARK(1 + z0466) :|: z1 >= 0, z = 1 + (1 + z0466) + z1 + z2, z0466 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U12(mark(z0464), z1268), z1, z2) + MARK(1 + z0464 + z1268) :|: z1268 >= 0, z1 >= 0, z0464 >= 0, z = 1 + (1 + z0464 + z1268) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U11(mark(z0463), z1267, z271), z1, z2) + MARK(1 + z0463 + z1267 + z271) :|: z1 >= 0, z271 >= 0, z = 1 + (1 + z0463 + z1267 + z271) + z1 + z2, z0463 >= 0, z2 >= 0, z1267 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(1 + mark(z0474), z1, z2) + MARK(1 + z0474) :|: z1 >= 0, z0474 >= 0, z = 1 + (1 + z0474) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__plus(mark(z0459), mark(z1265)), z1) + MARK(1 + z0459 + z1265) :|: z1 >= 0, z1265 >= 0, z = 1 + (1 + z0459 + z1265) + z1, z0459 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__isNatKind(z0461), z1) + MARK(1 + z0461) :|: z1 >= 0, z = 1 + (1 + z0461) + z1, z0461 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__isNat(z0453), z1) + MARK(1 + z0453) :|: z1 >= 0, z = 1 + (1 + z0453) + z1, z0453 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__and(mark(z0460), z1266), z1) + MARK(1 + z0460 + z1266) :|: z1 >= 0, z0460 >= 0, z = 1 + (1 + z0460 + z1266) + z1, z1266 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U41(mark(z0458), z1264, z270), z1) + MARK(1 + z0458 + z1264 + z270) :|: z = 1 + (1 + z0458 + z1264 + z270) + z1, z1 >= 0, z0458 >= 0, z270 >= 0, z1264 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U31(mark(z0457), z1263), z1) + MARK(1 + z0457 + z1263) :|: z1 >= 0, z0457 >= 0, z1263 >= 0, z = 1 + (1 + z0457 + z1263) + z1 MARK(z) -{ 1 }-> 1 + A__U31(a__U22(mark(z0456)), z1) + MARK(1 + z0456) :|: z1 >= 0, z = 1 + (1 + z0456) + z1, z0456 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U21(mark(z0455), z1262), z1) + MARK(1 + z0455 + z1262) :|: z = 1 + (1 + z0455 + z1262) + z1, z1 >= 0, z0455 >= 0, z1262 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U13(mark(z0454)), z1) + MARK(1 + z0454) :|: z = 1 + (1 + z0454) + z1, z1 >= 0, z0454 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U12(mark(z0452), z1261), z1) + MARK(1 + z0452 + z1261) :|: z = 1 + (1 + z0452 + z1261) + z1, z1261 >= 0, z1 >= 0, z0452 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U11(mark(z0451), z1260, z269), z1) + MARK(1 + z0451 + z1260 + z269) :|: z1 >= 0, z = 1 + (1 + z0451 + z1260 + z269) + z1, z269 >= 0, z0451 >= 0, z1260 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(1 + mark(z0462), z1) + MARK(1 + z0462) :|: z1 >= 0, z = 1 + (1 + z0462) + z1, z0462 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__plus(mark(z0447), mark(z1258)), z1) + MARK(1 + z0447 + z1258) :|: z0447 >= 0, z1258 >= 0, z1 >= 0, z = 1 + (1 + z0447 + z1258) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0449), z1) + MARK(1 + z0449) :|: z1 >= 0, z = 1 + (1 + z0449) + z1, z0449 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__isNat(z0441), z1) + MARK(1 + z0441) :|: z1 >= 0, z0441 >= 0, z = 1 + (1 + z0441) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__and(mark(z0448), z1259), z1) + MARK(1 + z0448 + z1259) :|: z = 1 + (1 + z0448 + z1259) + z1, z1 >= 0, z0448 >= 0, z1259 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U41(mark(z0446), z1257, z268), z1) + MARK(1 + z0446 + z1257 + z268) :|: z1 >= 0, z = 1 + (1 + z0446 + z1257 + z268) + z1, z268 >= 0, z0446 >= 0, z1257 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U31(mark(z0445), z1256), z1) + MARK(1 + z0445 + z1256) :|: z = 1 + (1 + z0445 + z1256) + z1, z1 >= 0, z0445 >= 0, z1256 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U22(mark(z0444)), z1) + MARK(1 + z0444) :|: z1 >= 0, z0444 >= 0, z = 1 + (1 + z0444) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z0443), z1255), z1) + MARK(1 + z0443 + z1255) :|: z = 1 + (1 + z0443 + z1255) + z1, z0443 >= 0, z1 >= 0, z1255 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U13(mark(z0442)), z1) + MARK(1 + z0442) :|: z1 >= 0, z = 1 + (1 + z0442) + z1, z0442 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U12(mark(z0440), z1254), z1) + MARK(1 + z0440 + z1254) :|: z1254 >= 0, z = 1 + (1 + z0440 + z1254) + z1, z1 >= 0, z0440 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z0439), z1253, z267), z1) + MARK(1 + z0439 + z1253 + z267) :|: z = 1 + (1 + z0439 + z1253 + z267) + z1, z1 >= 0, z1253 >= 0, z0439 >= 0, z267 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U21(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z0450), z1) + MARK(1 + z0450) :|: z1 >= 0, z0450 >= 0, z = 1 + (1 + z0450) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__plus(mark(z0435), mark(z1251)), z1) + MARK(1 + z0435 + z1251) :|: z1 >= 0, z0435 >= 0, z1251 >= 0, z = 1 + (1 + z0435 + z1251) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__isNatKind(z0437), z1) + MARK(1 + z0437) :|: z0437 >= 0, z1 >= 0, z = 1 + (1 + z0437) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__isNat(z0429), z1) + MARK(1 + z0429) :|: z = 1 + (1 + z0429) + z1, z1 >= 0, z0429 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__and(mark(z0436), z1252), z1) + MARK(1 + z0436 + z1252) :|: z1 >= 0, z0436 >= 0, z1252 >= 0, z = 1 + (1 + z0436 + z1252) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__U41(mark(z0434), z1250, z266), z1) + MARK(1 + z0434 + z1250 + z266) :|: z1250 >= 0, z1 >= 0, z = 1 + (1 + z0434 + z1250 + z266) + z1, z0434 >= 0, z266 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U31(mark(z0433), z1249), z1) + MARK(1 + z0433 + z1249) :|: z = 1 + (1 + z0433 + z1249) + z1, z0433 >= 0, z1 >= 0, z1249 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U22(mark(z0432)), z1) + MARK(1 + z0432) :|: z1 >= 0, z = 1 + (1 + z0432) + z1, z0432 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U21(mark(z0431), z1248), z1) + MARK(1 + z0431 + z1248) :|: z1 >= 0, z = 1 + (1 + z0431 + z1248) + z1, z0431 >= 0, z1248 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U13(mark(z0430)), z1) + MARK(1 + z0430) :|: z1 >= 0, z = 1 + (1 + z0430) + z1, z0430 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z0428), z1247), z1) + MARK(1 + z0428 + z1247) :|: z1 >= 0, z0428 >= 0, z = 1 + (1 + z0428 + z1247) + z1, z1247 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z0427), z1246, z265), z1) + MARK(1 + z0427 + z1246 + z265) :|: z1 >= 0, z0427 >= 0, z = 1 + (1 + z0427 + z1246 + z265) + z1, z1246 >= 0, z265 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z0438), z1) + MARK(1 + z0438) :|: z1 >= 0, z = 1 + (1 + z0438) + z1, z0438 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z0423), mark(z1244)), z1, z2) + MARK(1 + z0423 + z1244) :|: z = 1 + (1 + z0423 + z1244) + z1 + z2, z1 >= 0, z1244 >= 0, z0423 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__isNatKind(z0425), z1, z2) + MARK(1 + z0425) :|: z1 >= 0, z0425 >= 0, z = 1 + (1 + z0425) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__isNat(z0417), z1, z2) + MARK(1 + z0417) :|: z1 >= 0, z0417 >= 0, z = 1 + (1 + z0417) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__and(mark(z0424), z1245), z1, z2) + MARK(1 + z0424 + z1245) :|: z1 >= 0, z1245 >= 0, z = 1 + (1 + z0424 + z1245) + z1 + z2, z0424 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U41(mark(z0422), z1243, z264), z1, z2) + MARK(1 + z0422 + z1243 + z264) :|: z1 >= 0, z1243 >= 0, z = 1 + (1 + z0422 + z1243 + z264) + z1 + z2, z264 >= 0, z2 >= 0, z0422 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U31(mark(z0421), z1242), z1, z2) + MARK(1 + z0421 + z1242) :|: z1 >= 0, z1242 >= 0, z0421 >= 0, z2 >= 0, z = 1 + (1 + z0421 + z1242) + z1 + z2 MARK(z) -{ 1 }-> 1 + A__U11(a__U22(mark(z0420)), z1, z2) + MARK(1 + z0420) :|: z1 >= 0, z = 1 + (1 + z0420) + z1 + z2, z0420 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z0419), z1241), z1, z2) + MARK(1 + z0419 + z1241) :|: z1 >= 0, z = 1 + (1 + z0419 + z1241) + z1 + z2, z1241 >= 0, z0419 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U13(mark(z0418)), z1, z2) + MARK(1 + z0418) :|: z1 >= 0, z = 1 + (1 + z0418) + z1 + z2, z0418 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z0416), z1240), z1, z2) + MARK(1 + z0416 + z1240) :|: z1 >= 0, z0416 >= 0, z = 1 + (1 + z0416 + z1240) + z1 + z2, z1240 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z0415), z1239, z263), z1, z2) + MARK(1 + z0415 + z1239 + z263) :|: z = 1 + (1 + z0415 + z1239 + z263) + z1 + z2, z1 >= 0, z0415 >= 0, z1239 >= 0, z263 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z0426), z1, z2) + MARK(1 + z0426) :|: z1 >= 0, z0426 >= 0, z2 >= 0, z = 1 + (1 + z0426) + z1 + z2 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__plus(mark(z0867), mark(z1503)), z1) + MARK(1 + z0867 + z1503) :|: z1 >= 0, z0867 >= 0, z = 1 + (1 + z0867 + z1503) + z1, z1503 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0869), z1) + MARK(1 + z0869) :|: z1 >= 0, z0869 >= 0, z = 1 + (1 + z0869) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__isNat(z0861), z1) + MARK(1 + z0861) :|: z1 >= 0, z = 1 + (1 + z0861) + z1, z0861 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z0868), z1504), z1) + MARK(1 + z0868 + z1504) :|: z0868 >= 0, z1 >= 0, z = 1 + (1 + z0868 + z1504) + z1, z1504 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U41(mark(z0866), z1502, z2138), z1) + MARK(1 + z0866 + z1502 + z2138) :|: z1 >= 0, z1502 >= 0, z2138 >= 0, z0866 >= 0, z = 1 + (1 + z0866 + z1502 + z2138) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U31(mark(z0865), z1501), z1) + MARK(1 + z0865 + z1501) :|: z1 >= 0, z1501 >= 0, z = 1 + (1 + z0865 + z1501) + z1, z0865 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U22(mark(z0864)), z1) + MARK(1 + z0864) :|: z = 1 + (1 + z0864) + z1, z0864 >= 0, z1 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U21(mark(z0863), z1500), z1) + MARK(1 + z0863 + z1500) :|: z1 >= 0, z0863 >= 0, z1500 >= 0, z = 1 + (1 + z0863 + z1500) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U13(mark(z0862)), z1) + MARK(1 + z0862) :|: z1 >= 0, z0862 >= 0, z = 1 + (1 + z0862) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U12(mark(z0860), z1499), z1) + MARK(1 + z0860 + z1499) :|: z0860 >= 0, z1 >= 0, z = 1 + (1 + z0860 + z1499) + z1, z1499 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U11(mark(z0859), z1498, z2137), z1) + MARK(1 + z0859 + z1498 + z2137) :|: z1 >= 0, z2137 >= 0, z1498 >= 0, z = 1 + (1 + z0859 + z1498 + z2137) + z1, z0859 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z0870), z1) + MARK(1 + z0870) :|: z = 1 + (1 + z0870) + z1, z0870 >= 0, z1 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U21(a__isNatKind(z0872), z0872), z1) :|: z' = 1 + z0872, z1 >= 0, z = 1, z0872 >= 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U11(a__and(a__isNatKind(z0871), 1 + z1505), z0871, z1505), z1) :|: z1 >= 0, z = 1, z0871 >= 0, z' = 1 + z0871 + z1505, z1505 >= 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1 + z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U12(z, z') -{ 0 }-> a__U13(a__U21(a__isNatKind(z0874), z0874)) :|: z0874 >= 0, z = 1, z' = 1 + z0874 a__U12(z, z') -{ 0 }-> a__U13(a__U11(a__and(a__isNatKind(z0873), 1 + z1506), z0873, z1506)) :|: z1506 >= 0, z = 1, z' = 1 + z0873 + z1506, z0873 >= 0 a__U12(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U12(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = 1 a__U12(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U12(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U12(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U12(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U12(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U12(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U12(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U12(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U13(z) -{ 0 }-> 1 :|: z = 1 a__U13(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U13(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z0876), z0876)) :|: z = 1, z' = 1 + z0876, z0876 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__and(a__isNatKind(z0875), 1 + z1507), z0875, z1507)) :|: z = 1, z1507 >= 0, z' = 1 + z0875 + z1507, z0875 >= 0 a__U21(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U21(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = 1 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U21(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U21(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U21(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z) -{ 0 }-> 1 :|: z = 1 a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z01072), 1 + z01072) :|: z01072 >= 0, z = 1 + (1 + z01072) a__isNat(z) -{ 0 }-> a__U21(a__and(a__isNatKind(z01071), 1 + z1621), 1 + z01071 + z1621) :|: z = 1 + (1 + z01071 + z1621), z01071 >= 0, z1621 >= 0 a__isNat(z) -{ 0 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + z0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z01070), 1 + z1), 1 + z01070, z1) :|: z01070 >= 0, z = 1 + (1 + z01070) + z1, z1 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__and(a__isNatKind(z01069), 1 + z1620), 1 + z1), 1 + z01069 + z1620, z1) :|: z1 >= 0, z1620 >= 0, z01069 >= 0, z = 1 + (1 + z01069 + z1620) + z1 a__isNat(z) -{ 0 }-> a__U11(a__and(1, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNat(z) -{ 0 }-> a__U11(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__U11(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__and(a__isNatKind(z01074), 1 + z1) :|: z01074 >= 0, z1 >= 0, z = 1 + (1 + z01074) + z1 a__isNatKind(z) -{ 0 }-> a__and(a__and(a__isNatKind(z01073), 1 + z1622), 1 + z1) :|: z1622 >= 0, z1 >= 0, z01073 >= 0, z = 1 + (1 + z01073 + z1622) + z1 a__isNatKind(z) -{ 0 }-> a__and(1, 1 + z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(z01078), z01078), 1 + (1 + z01078)), 1 + (1 + z0) + (1 + z0)), 1 + z01078, z0) :|: z01078 >= 0, z = z0, z' = 1 + (1 + z01078), z0 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z01077), 1 + z1624), z01077, z1624), 1 + (1 + z01077 + z1624)), 1 + (1 + z0) + (1 + z0)), 1 + z01077 + z1624, z0) :|: z = z0, z1624 >= 0, z' = 1 + (1 + z01077 + z1624), z0 >= 0, z01077 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + z0) + (1 + z0)), 0, z0) :|: z = z0, z' = 1 + 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(0, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(1 + z1, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U31(a__and(a__U21(a__isNatKind(z01076), z01076), 1 + (1 + z01076)), 1 + z01076) :|: z = 1 + z01076, z01076 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(z01075), 1 + z1623), z01075, z1623), 1 + (1 + z01075 + z1623)), 1 + z01075 + z1623) :|: z01075 >= 0, z1623 >= 0, z = 1 + z01075 + z1623, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(0, 1 + z0), z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(1 + z0, 1 + z0), z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__and(a__plus(mark(z01363), mark(z1791)), z1) :|: z = 1 + (1 + z01363 + z1791) + z1, z1 >= 0, z01363 >= 0, z1791 >= 0 mark(z) -{ 0 }-> a__and(a__isNatKind(z01365), z1) :|: z = 1 + (1 + z01365) + z1, z1 >= 0, z01365 >= 0 mark(z) -{ 0 }-> a__and(a__isNat(z01357), z1) :|: z1 >= 0, z = 1 + (1 + z01357) + z1, z01357 >= 0 mark(z) -{ 0 }-> a__and(a__and(mark(z01364), z1792), z1) :|: z01364 >= 0, z1 >= 0, z = 1 + (1 + z01364 + z1792) + z1, z1792 >= 0 mark(z) -{ 0 }-> a__and(a__U41(mark(z01362), z1790, z2218), z1) :|: z2218 >= 0, z1790 >= 0, z1 >= 0, z = 1 + (1 + z01362 + z1790 + z2218) + z1, z01362 >= 0 mark(z) -{ 0 }-> a__and(a__U31(mark(z01361), z1789), z1) :|: z1 >= 0, z01361 >= 0, z = 1 + (1 + z01361 + z1789) + z1, z1789 >= 0 mark(z) -{ 0 }-> a__and(a__U22(mark(z01360)), z1) :|: z01360 >= 0, z1 >= 0, z = 1 + (1 + z01360) + z1 mark(z) -{ 0 }-> a__and(a__U21(mark(z01359), z1788), z1) :|: z1788 >= 0, z1 >= 0, z = 1 + (1 + z01359 + z1788) + z1, z01359 >= 0 mark(z) -{ 0 }-> a__and(a__U13(mark(z01358)), z1) :|: z1 >= 0, z01358 >= 0, z = 1 + (1 + z01358) + z1 mark(z) -{ 0 }-> a__and(a__U12(mark(z01356), z1787), z1) :|: z1 >= 0, z1787 >= 0, z = 1 + (1 + z01356 + z1787) + z1, z01356 >= 0 mark(z) -{ 0 }-> a__and(a__U11(mark(z01355), z1786, z2217), z1) :|: z1 >= 0, z2217 >= 0, z1786 >= 0, z01355 >= 0, z = 1 + (1 + z01355 + z1786 + z2217) + z1 mark(z) -{ 0 }-> a__and(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(1 + mark(z01366), z1) :|: z1 >= 0, z01366 >= 0, z = 1 + (1 + z01366) + z1 mark(z) -{ 0 }-> a__U41(a__plus(mark(z01159), mark(z1672)), z1, z2) :|: z1 >= 0, z01159 >= 0, z = 1 + (1 + z01159 + z1672) + z1 + z2, z1672 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__isNatKind(z01161), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01161) + z1 + z2, z01161 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__isNat(z01153), z1, z2) :|: z1 >= 0, z01153 >= 0, z = 1 + (1 + z01153) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__and(mark(z01160), z1673), z1, z2) :|: z = 1 + (1 + z01160 + z1673) + z1 + z2, z1 >= 0, z01160 >= 0, z1673 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U41(mark(z01158), z1671, z2184), z1, z2) :|: z1671 >= 0, z1 >= 0, z01158 >= 0, z = 1 + (1 + z01158 + z1671 + z2184) + z1 + z2, z2184 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U31(mark(z01157), z1670), z1, z2) :|: z1670 >= 0, z1 >= 0, z = 1 + (1 + z01157 + z1670) + z1 + z2, z01157 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U22(mark(z01156)), z1, z2) :|: z1 >= 0, z01156 >= 0, z2 >= 0, z = 1 + (1 + z01156) + z1 + z2 mark(z) -{ 0 }-> a__U41(a__U21(mark(z01155), z1669), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01155 + z1669) + z1 + z2, z1669 >= 0, z01155 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U13(mark(z01154)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01154) + z1 + z2, z01154 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U12(mark(z01152), z1668), z1, z2) :|: z1668 >= 0, z1 >= 0, z = 1 + (1 + z01152 + z1668) + z1 + z2, z01152 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U11(mark(z01151), z1667, z2183), z1, z2) :|: z1 >= 0, z1667 >= 0, z01151 >= 0, z = 1 + (1 + z01151 + z1667 + z2183) + z1 + z2, z2183 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(1 + mark(z01162), z1, z2) :|: z1 >= 0, z01162 >= 0, z = 1 + (1 + z01162) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U31(a__plus(mark(z01147), mark(z1665)), z1) :|: z = 1 + (1 + z01147 + z1665) + z1, z1 >= 0, z1665 >= 0, z01147 >= 0 mark(z) -{ 0 }-> a__U31(a__isNatKind(z01149), z1) :|: z01149 >= 0, z1 >= 0, z = 1 + (1 + z01149) + z1 mark(z) -{ 0 }-> a__U31(a__isNat(z01141), z1) :|: z = 1 + (1 + z01141) + z1, z01141 >= 0, z1 >= 0 mark(z) -{ 0 }-> a__U31(a__and(mark(z01148), z1666), z1) :|: z1 >= 0, z01148 >= 0, z1666 >= 0, z = 1 + (1 + z01148 + z1666) + z1 mark(z) -{ 0 }-> a__U31(a__U41(mark(z01146), z1664, z2182), z1) :|: z1664 >= 0, z1 >= 0, z = 1 + (1 + z01146 + z1664 + z2182) + z1, z2182 >= 0, z01146 >= 0 mark(z) -{ 0 }-> a__U31(a__U31(mark(z01145), z1663), z1) :|: z01145 >= 0, z1 >= 0, z = 1 + (1 + z01145 + z1663) + z1, z1663 >= 0 mark(z) -{ 0 }-> a__U31(a__U22(mark(z01144)), z1) :|: z1 >= 0, z01144 >= 0, z = 1 + (1 + z01144) + z1 mark(z) -{ 0 }-> a__U31(a__U21(mark(z01143), z1662), z1) :|: z1 >= 0, z1662 >= 0, z = 1 + (1 + z01143 + z1662) + z1, z01143 >= 0 mark(z) -{ 0 }-> a__U31(a__U13(mark(z01142)), z1) :|: z1 >= 0, z = 1 + (1 + z01142) + z1, z01142 >= 0 mark(z) -{ 0 }-> a__U31(a__U12(mark(z01140), z1661), z1) :|: z1 >= 0, z = 1 + (1 + z01140 + z1661) + z1, z01140 >= 0, z1661 >= 0 mark(z) -{ 0 }-> a__U31(a__U11(mark(z01139), z1660, z2181), z1) :|: z1660 >= 0, z2181 >= 0, z1 >= 0, z = 1 + (1 + z01139 + z1660 + z2181) + z1, z01139 >= 0 mark(z) -{ 0 }-> a__U31(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U31(1 + mark(z01150), z1) :|: z1 >= 0, z = 1 + (1 + z01150) + z1, z01150 >= 0 mark(z) -{ 0 }-> a__U22(a__plus(mark(z01135), mark(z1658))) :|: z01135 >= 0, z1658 >= 0, z = 1 + (1 + z01135 + z1658) mark(z) -{ 0 }-> a__U22(a__isNatKind(z01137)) :|: z = 1 + (1 + z01137), z01137 >= 0 mark(z) -{ 0 }-> a__U22(a__isNat(z01129)) :|: z01129 >= 0, z = 1 + (1 + z01129) mark(z) -{ 0 }-> a__U22(a__and(mark(z01136), z1659)) :|: z1659 >= 0, z = 1 + (1 + z01136 + z1659), z01136 >= 0 mark(z) -{ 0 }-> a__U22(a__U41(mark(z01134), z1657, z2180)) :|: z01134 >= 0, z1657 >= 0, z2180 >= 0, z = 1 + (1 + z01134 + z1657 + z2180) mark(z) -{ 0 }-> a__U22(a__U31(mark(z01133), z1656)) :|: z = 1 + (1 + z01133 + z1656), z1656 >= 0, z01133 >= 0 mark(z) -{ 0 }-> a__U22(a__U22(mark(z01132))) :|: z = 1 + (1 + z01132), z01132 >= 0 mark(z) -{ 0 }-> a__U22(a__U21(mark(z01131), z1655)) :|: z01131 >= 0, z = 1 + (1 + z01131 + z1655), z1655 >= 0 mark(z) -{ 0 }-> a__U22(a__U13(mark(z01130))) :|: z01130 >= 0, z = 1 + (1 + z01130) mark(z) -{ 0 }-> a__U22(a__U12(mark(z01128), z1654)) :|: z1654 >= 0, z01128 >= 0, z = 1 + (1 + z01128 + z1654) mark(z) -{ 0 }-> a__U22(a__U11(mark(z01127), z1653, z2179)) :|: z2179 >= 0, z01127 >= 0, z1653 >= 0, z = 1 + (1 + z01127 + z1653 + z2179) mark(z) -{ 0 }-> a__U22(1 + mark(z01138)) :|: z01138 >= 0, z = 1 + (1 + z01138) mark(z) -{ 0 }-> a__U21(a__plus(mark(z01123), mark(z1651)), z1) :|: z1 >= 0, z01123 >= 0, z1651 >= 0, z = 1 + (1 + z01123 + z1651) + z1 mark(z) -{ 0 }-> a__U21(a__isNatKind(z01125), z1) :|: z1 >= 0, z = 1 + (1 + z01125) + z1, z01125 >= 0 mark(z) -{ 0 }-> a__U21(a__isNat(z01117), z1) :|: z1 >= 0, z = 1 + (1 + z01117) + z1, z01117 >= 0 mark(z) -{ 0 }-> a__U21(a__and(mark(z01124), z1652), z1) :|: z1 >= 0, z01124 >= 0, z1652 >= 0, z = 1 + (1 + z01124 + z1652) + z1 mark(z) -{ 0 }-> a__U21(a__U41(mark(z01122), z1650, z2178), z1) :|: z2178 >= 0, z1650 >= 0, z1 >= 0, z01122 >= 0, z = 1 + (1 + z01122 + z1650 + z2178) + z1 mark(z) -{ 0 }-> a__U21(a__U31(mark(z01121), z1649), z1) :|: z1 >= 0, z01121 >= 0, z1649 >= 0, z = 1 + (1 + z01121 + z1649) + z1 mark(z) -{ 0 }-> a__U21(a__U22(mark(z01120)), z1) :|: z = 1 + (1 + z01120) + z1, z1 >= 0, z01120 >= 0 mark(z) -{ 0 }-> a__U21(a__U21(mark(z01119), z1648), z1) :|: z1 >= 0, z1648 >= 0, z01119 >= 0, z = 1 + (1 + z01119 + z1648) + z1 mark(z) -{ 0 }-> a__U21(a__U13(mark(z01118)), z1) :|: z = 1 + (1 + z01118) + z1, z1 >= 0, z01118 >= 0 mark(z) -{ 0 }-> a__U21(a__U12(mark(z01116), z1647), z1) :|: z1647 >= 0, z1 >= 0, z = 1 + (1 + z01116 + z1647) + z1, z01116 >= 0 mark(z) -{ 0 }-> a__U21(a__U11(mark(z01115), z1646, z2177), z1) :|: z1 >= 0, z1646 >= 0, z2177 >= 0, z = 1 + (1 + z01115 + z1646 + z2177) + z1, z01115 >= 0 mark(z) -{ 0 }-> a__U21(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U21(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U21(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U21(1 + mark(z01126), z1) :|: z1 >= 0, z = 1 + (1 + z01126) + z1, z01126 >= 0 mark(z) -{ 0 }-> a__U13(a__plus(mark(z01111), mark(z1644))) :|: z = 1 + (1 + z01111 + z1644), z01111 >= 0, z1644 >= 0 mark(z) -{ 0 }-> a__U13(a__isNatKind(z01113)) :|: z = 1 + (1 + z01113), z01113 >= 0 mark(z) -{ 0 }-> a__U13(a__isNat(z01105)) :|: z = 1 + (1 + z01105), z01105 >= 0 mark(z) -{ 0 }-> a__U13(a__and(mark(z01112), z1645)) :|: z01112 >= 0, z1645 >= 0, z = 1 + (1 + z01112 + z1645) mark(z) -{ 0 }-> a__U13(a__U41(mark(z01110), z1643, z2176)) :|: z1643 >= 0, z01110 >= 0, z = 1 + (1 + z01110 + z1643 + z2176), z2176 >= 0 mark(z) -{ 0 }-> a__U13(a__U31(mark(z01109), z1642)) :|: z = 1 + (1 + z01109 + z1642), z01109 >= 0, z1642 >= 0 mark(z) -{ 0 }-> a__U13(a__U22(mark(z01108))) :|: z = 1 + (1 + z01108), z01108 >= 0 mark(z) -{ 0 }-> a__U13(a__U21(mark(z01107), z1641)) :|: z = 1 + (1 + z01107 + z1641), z01107 >= 0, z1641 >= 0 mark(z) -{ 0 }-> a__U13(a__U13(mark(z01106))) :|: z = 1 + (1 + z01106), z01106 >= 0 mark(z) -{ 0 }-> a__U13(a__U12(mark(z01104), z1640)) :|: z01104 >= 0, z1640 >= 0, z = 1 + (1 + z01104 + z1640) mark(z) -{ 0 }-> a__U13(a__U11(mark(z01103), z1639, z2175)) :|: z01103 >= 0, z1639 >= 0, z2175 >= 0, z = 1 + (1 + z01103 + z1639 + z2175) mark(z) -{ 0 }-> a__U13(1 + mark(z01114)) :|: z01114 >= 0, z = 1 + (1 + z01114) mark(z) -{ 0 }-> a__U12(a__plus(mark(z01099), mark(z1637)), z1) :|: z01099 >= 0, z1 >= 0, z1637 >= 0, z = 1 + (1 + z01099 + z1637) + z1 mark(z) -{ 0 }-> a__U12(a__isNatKind(z01101), z1) :|: z1 >= 0, z = 1 + (1 + z01101) + z1, z01101 >= 0 mark(z) -{ 0 }-> a__U12(a__isNat(z01093), z1) :|: z1 >= 0, z = 1 + (1 + z01093) + z1, z01093 >= 0 mark(z) -{ 0 }-> a__U12(a__and(mark(z01100), z1638), z1) :|: z1 >= 0, z01100 >= 0, z1638 >= 0, z = 1 + (1 + z01100 + z1638) + z1 mark(z) -{ 0 }-> a__U12(a__U41(mark(z01098), z1636, z2174), z1) :|: z2174 >= 0, z01098 >= 0, z1 >= 0, z1636 >= 0, z = 1 + (1 + z01098 + z1636 + z2174) + z1 mark(z) -{ 0 }-> a__U12(a__U31(mark(z01097), z1635), z1) :|: z = 1 + (1 + z01097 + z1635) + z1, z1 >= 0, z1635 >= 0, z01097 >= 0 mark(z) -{ 0 }-> a__U12(a__U22(mark(z01096)), z1) :|: z = 1 + (1 + z01096) + z1, z1 >= 0, z01096 >= 0 mark(z) -{ 0 }-> a__U12(a__U21(mark(z01095), z1634), z1) :|: z1 >= 0, z01095 >= 0, z = 1 + (1 + z01095 + z1634) + z1, z1634 >= 0 mark(z) -{ 0 }-> a__U12(a__U13(mark(z01094)), z1) :|: z = 1 + (1 + z01094) + z1, z1 >= 0, z01094 >= 0 mark(z) -{ 0 }-> a__U12(a__U12(mark(z01092), z1633), z1) :|: z = 1 + (1 + z01092 + z1633) + z1, z1 >= 0, z01092 >= 0, z1633 >= 0 mark(z) -{ 0 }-> a__U12(a__U11(mark(z01091), z1632, z2173), z1) :|: z1 >= 0, z01091 >= 0, z = 1 + (1 + z01091 + z1632 + z2173) + z1, z2173 >= 0, z1632 >= 0 mark(z) -{ 0 }-> a__U12(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(1 + mark(z01102), z1) :|: z1 >= 0, z01102 >= 0, z = 1 + (1 + z01102) + z1 mark(z) -{ 0 }-> a__U11(a__plus(mark(z01087), mark(z1630)), z1, z2) :|: z1 >= 0, z1630 >= 0, z2 >= 0, z = 1 + (1 + z01087 + z1630) + z1 + z2, z01087 >= 0 mark(z) -{ 0 }-> a__U11(a__isNatKind(z01089), z1, z2) :|: z1 >= 0, z01089 >= 0, z = 1 + (1 + z01089) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__isNat(z01081), z1, z2) :|: z1 >= 0, z01081 >= 0, z2 >= 0, z = 1 + (1 + z01081) + z1 + z2 mark(z) -{ 0 }-> a__U11(a__and(mark(z01088), z1631), z1, z2) :|: z = 1 + (1 + z01088 + z1631) + z1 + z2, z01088 >= 0, z1 >= 0, z1631 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U41(mark(z01086), z1629, z2172), z1, z2) :|: z1 >= 0, z2172 >= 0, z01086 >= 0, z = 1 + (1 + z01086 + z1629 + z2172) + z1 + z2, z1629 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U31(mark(z01085), z1628), z1, z2) :|: z1 >= 0, z01085 >= 0, z1628 >= 0, z = 1 + (1 + z01085 + z1628) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U22(mark(z01084)), z1, z2) :|: z01084 >= 0, z1 >= 0, z = 1 + (1 + z01084) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U21(mark(z01083), z1627), z1, z2) :|: z1 >= 0, z1627 >= 0, z01083 >= 0, z = 1 + (1 + z01083 + z1627) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U13(mark(z01082)), z1, z2) :|: z1 >= 0, z01082 >= 0, z = 1 + (1 + z01082) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U12(mark(z01080), z1626), z1, z2) :|: z1626 >= 0, z01080 >= 0, z1 >= 0, z = 1 + (1 + z01080 + z1626) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z01079), z1625, z2171), z1, z2) :|: z = 1 + (1 + z01079 + z1625 + z2171) + z1 + z2, z1 >= 0, z1625 >= 0, z2171 >= 0, z01079 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1 + mark(z01090), z1, z2) :|: z = 1 + (1 + z01090) + z1 + z2, z1 >= 0, z01090 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 1 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (67) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 1, z' >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z - 2), 1 + (z - 2)) + A__ISNATKIND(1 + (z - 2)) :|: z - 2 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__and(a__isNatKind(z0391), 1 + z1227), 1 + z0391 + z1227) + A__ISNATKIND(1 + z0391 + z1227) :|: z = 1 + (1 + z0391 + z1227), z0391 >= 0, z1227 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z - 1) + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + (z - 1), z - 1) + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(a__isNatKind(z0386), 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0386), 1 + z1), 1 + z0386, z1) + A__AND(1 + (1 + z0386), 1 + z1) + A__ISNATKIND(1 + z0386) :|: z0386 >= 0, z = 1 + (1 + z0386) + z1, z1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__and(a__isNatKind(z0385), 1 + z1224), 1 + z1), 1 + z0385 + z1224, z1) + A__AND(1 + (1 + z0385 + z1224), 1 + z1) + A__ISNATKIND(1 + z0385 + z1224) :|: z1 >= 0, z1224 >= 0, z0385 >= 0, z = 1 + (1 + z0385 + z1224) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + (z - 1)), 0, z - 1) + A__AND(1, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + (z - 1)), 0, z - 1) + A__AND(0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1, 1 + (z - 1)), 0, z - 1) + A__AND(1 + 0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), 1 + z0390, z1) + A__AND(a__isNatKind(z0390), 1 + z1) + A__ISNATKIND(1 + z0390) :|: z1 >= 0, z = 1 + (1 + z0390) + z1, z0390 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + z1), 1 + z0389 + z1226, z1) + A__AND(a__and(a__isNatKind(z0389), 1 + z1226), 1 + z1) + A__ISNATKIND(1 + z0389 + z1226) :|: z1226 >= 0, z1 >= 0, z = 1 + (1 + z0389 + z1226) + z1, z0389 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(0, 1 + (z - 1)), 0, z - 1) + A__AND(1, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + 0, 1 + (z - 1)), 0, z - 1) + A__AND(1, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + (1 + z0388), 1 + z1), 1 + z0388, z1) + A__AND(a__isNatKind(z0388), 1 + z1) + A__ISNATKIND(1 + z0388) :|: z = 1 + (1 + z0388) + z1, z1 >= 0, z0388 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(1 + (1 + z0387 + z1225), 1 + z1), 1 + z0387 + z1225, z1) + A__AND(a__and(a__isNatKind(z0387), 1 + z1225), 1 + z1) + A__ISNATKIND(1 + z0387 + z1225) :|: z1 >= 0, z = 1 + (1 + z0387 + z1225) + z1, z0387 >= 0, z1225 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0394), 1 + z1) + A__ISNATKIND(1 + z0394) :|: z1 >= 0, z = 1 + (1 + z0394) + z1, z0394 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(a__and(a__isNatKind(z0393), 1 + z1228), 1 + z1) + A__ISNATKIND(1 + z0393 + z1228) :|: z1 >= 0, z1228 >= 0, z = 1 + (1 + z0393 + z1228) + z1, z0393 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(1, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))), 1 + (z - 1)) + A__AND(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))) + A__ISNAT(1 + (z - 1)) :|: z - 1 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))), 1 + (z - 1)) + A__AND(0, 1 + (1 + (z - 1))) + A__ISNAT(1 + (z - 1)) :|: z - 1 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))), 1 + (z - 1)) + A__AND(1 + (1 + (z - 1)), 1 + (1 + (z - 1))) + A__ISNAT(1 + (z - 1)) :|: z - 1 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(0, 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__U11(a__and(a__isNatKind(z0395), 1 + z1229), z0395, z1229), 1 + (1 + z0395 + z1229)), 1 + z0395 + z1229) + A__AND(1 + (1 + z0395 + z1229), 1 + (1 + z0395 + z1229)) + A__ISNAT(1 + z0395 + z1229) :|: z = 1 + z0395 + z1229, z0395 >= 0, z1229 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(0, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1, 1 + 0), 0) + A__AND(1 + 0, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + z), z) + A__AND(0, 1 + z) + A__ISNAT(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + z), z) + A__AND(1 + z, 1 + z) + A__ISNAT(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + (1 + (z - 1))), 1 + (z - 1)) + A__AND(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))) + A__ISNAT(1 + (z - 1)) :|: z - 1 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(0, 1 + (1 + z0399 + z1231)), 1 + z0399 + z1231) + A__AND(a__U11(a__and(a__isNatKind(z0399), 1 + z1231), z0399, z1231), 1 + (1 + z0399 + z1231)) + A__ISNAT(1 + z0399 + z1231) :|: z = 1 + z0399 + z1231, z1231 >= 0, z0399 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + z, 1 + z), z) + A__AND(0, 1 + z) + A__ISNAT(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + z, 1 + z), z) + A__AND(1 + z, 1 + z) + A__ISNAT(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + 0, 1 + 0), 0) + A__AND(1, 1 + 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + (1 + (z - 1)), 1 + (1 + (z - 1))), 1 + (z - 1)) + A__AND(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))) + A__ISNAT(1 + (z - 1)) :|: z - 1 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(1 + (1 + z0397 + z1230), 1 + (1 + z0397 + z1230)), 1 + z0397 + z1230) + A__AND(a__U11(a__and(a__isNatKind(z0397), 1 + z1230), z0397, z1230), 1 + (1 + z0397 + z1230)) + A__ISNAT(1 + z0397 + z1230) :|: z0397 >= 0, z = 1 + z0397 + z1230, z1230 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__and(a__and(a__isNat(z' - 1), 1 + (z' - 1)), 1 + (1 + z) + (1 + z)), z' - 1, z) + A__AND(a__and(a__isNat(z' - 1), 1 + (z' - 1)), 1 + (1 + z) + (1 + z)) + A__AND(a__isNat(z' - 1), 1 + (z' - 1)) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U21(a__isNatKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z'' >= 0, z = 1, z' - 1 >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U11(a__and(a__isNatKind(z0'), 1 + z1'), z0', z1'), z'') + A__ISNAT(1 + z0' + z1') :|: z'' >= 0, z = 1, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1' A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z'') + A__ISNAT(0) :|: z'' >= 0, z = 1, z' = 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(0, z'') + A__ISNAT(z') :|: z'' >= 0, z = 1, z' >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1 + z', z'') + A__ISNAT(z') :|: z'' >= 0, z = 1, z' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__ISNAT(z') :|: z = 1, z' >= 0 A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z') :|: z = 1, z' >= 0 A__U31(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 1, z' >= 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z') :|: z'' >= 0, z = 1, z' >= 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__plus(mark(z0471), mark(z1272)), z1, z2) + MARK(1 + z0471 + z1272) :|: z0471 >= 0, z1 >= 0, z1272 >= 0, z = 1 + (1 + z0471 + z1272) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__isNatKind(z0473), z1, z2) + MARK(1 + z0473) :|: z1 >= 0, z = 1 + (1 + z0473) + z1 + z2, z0473 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__isNat(z0465), z1, z2) + MARK(1 + z0465) :|: z1 >= 0, z0465 >= 0, z = 1 + (1 + z0465) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__and(mark(z0472), z1273), z1, z2) + MARK(1 + z0472 + z1273) :|: z1 >= 0, z1273 >= 0, z2 >= 0, z = 1 + (1 + z0472 + z1273) + z1 + z2, z0472 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U41(mark(z0470), z1271, z272), z1, z2) + MARK(1 + z0470 + z1271 + z272) :|: z1271 >= 0, z1 >= 0, z0470 >= 0, z272 >= 0, z = 1 + (1 + z0470 + z1271 + z272) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U31(mark(z0469), z1270), z1, z2) + MARK(1 + z0469 + z1270) :|: z1 >= 0, z = 1 + (1 + z0469 + z1270) + z1 + z2, z0469 >= 0, z1270 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U22(mark(z0468)), z1, z2) + MARK(1 + z0468) :|: z = 1 + (1 + z0468) + z1 + z2, z1 >= 0, z0468 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U21(mark(z0467), z1269), z1, z2) + MARK(1 + z0467 + z1269) :|: z1 >= 0, z1269 >= 0, z0467 >= 0, z = 1 + (1 + z0467 + z1269) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U13(mark(z0466)), z1, z2) + MARK(1 + z0466) :|: z1 >= 0, z = 1 + (1 + z0466) + z1 + z2, z0466 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U12(mark(z0464), z1268), z1, z2) + MARK(1 + z0464 + z1268) :|: z1268 >= 0, z1 >= 0, z0464 >= 0, z = 1 + (1 + z0464 + z1268) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(a__U11(mark(z0463), z1267, z271), z1, z2) + MARK(1 + z0463 + z1267 + z271) :|: z1 >= 0, z271 >= 0, z = 1 + (1 + z0463 + z1267 + z271) + z1 + z2, z0463 >= 0, z2 >= 0, z1267 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(1 + mark(z0474), z1, z2) + MARK(1 + z0474) :|: z1 >= 0, z0474 >= 0, z = 1 + (1 + z0474) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__plus(mark(z0459), mark(z1265)), z1) + MARK(1 + z0459 + z1265) :|: z1 >= 0, z1265 >= 0, z = 1 + (1 + z0459 + z1265) + z1, z0459 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__isNatKind(z0461), z1) + MARK(1 + z0461) :|: z1 >= 0, z = 1 + (1 + z0461) + z1, z0461 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__isNat(z0453), z1) + MARK(1 + z0453) :|: z1 >= 0, z = 1 + (1 + z0453) + z1, z0453 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__and(mark(z0460), z1266), z1) + MARK(1 + z0460 + z1266) :|: z1 >= 0, z0460 >= 0, z = 1 + (1 + z0460 + z1266) + z1, z1266 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U41(mark(z0458), z1264, z270), z1) + MARK(1 + z0458 + z1264 + z270) :|: z = 1 + (1 + z0458 + z1264 + z270) + z1, z1 >= 0, z0458 >= 0, z270 >= 0, z1264 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U31(mark(z0457), z1263), z1) + MARK(1 + z0457 + z1263) :|: z1 >= 0, z0457 >= 0, z1263 >= 0, z = 1 + (1 + z0457 + z1263) + z1 MARK(z) -{ 1 }-> 1 + A__U31(a__U22(mark(z0456)), z1) + MARK(1 + z0456) :|: z1 >= 0, z = 1 + (1 + z0456) + z1, z0456 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U21(mark(z0455), z1262), z1) + MARK(1 + z0455 + z1262) :|: z = 1 + (1 + z0455 + z1262) + z1, z1 >= 0, z0455 >= 0, z1262 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U13(mark(z0454)), z1) + MARK(1 + z0454) :|: z = 1 + (1 + z0454) + z1, z1 >= 0, z0454 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U12(mark(z0452), z1261), z1) + MARK(1 + z0452 + z1261) :|: z = 1 + (1 + z0452 + z1261) + z1, z1261 >= 0, z1 >= 0, z0452 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(a__U11(mark(z0451), z1260, z269), z1) + MARK(1 + z0451 + z1260 + z269) :|: z1 >= 0, z = 1 + (1 + z0451 + z1260 + z269) + z1, z269 >= 0, z0451 >= 0, z1260 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(1 + mark(z0462), z1) + MARK(1 + z0462) :|: z1 >= 0, z = 1 + (1 + z0462) + z1, z0462 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__plus(mark(z0447), mark(z1258)), z1) + MARK(1 + z0447 + z1258) :|: z0447 >= 0, z1258 >= 0, z1 >= 0, z = 1 + (1 + z0447 + z1258) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0449), z1) + MARK(1 + z0449) :|: z1 >= 0, z = 1 + (1 + z0449) + z1, z0449 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__isNat(z0441), z1) + MARK(1 + z0441) :|: z1 >= 0, z0441 >= 0, z = 1 + (1 + z0441) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__and(mark(z0448), z1259), z1) + MARK(1 + z0448 + z1259) :|: z = 1 + (1 + z0448 + z1259) + z1, z1 >= 0, z0448 >= 0, z1259 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U41(mark(z0446), z1257, z268), z1) + MARK(1 + z0446 + z1257 + z268) :|: z1 >= 0, z = 1 + (1 + z0446 + z1257 + z268) + z1, z268 >= 0, z0446 >= 0, z1257 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U31(mark(z0445), z1256), z1) + MARK(1 + z0445 + z1256) :|: z = 1 + (1 + z0445 + z1256) + z1, z1 >= 0, z0445 >= 0, z1256 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U22(mark(z0444)), z1) + MARK(1 + z0444) :|: z1 >= 0, z0444 >= 0, z = 1 + (1 + z0444) + z1 MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z0443), z1255), z1) + MARK(1 + z0443 + z1255) :|: z = 1 + (1 + z0443 + z1255) + z1, z0443 >= 0, z1 >= 0, z1255 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U13(mark(z0442)), z1) + MARK(1 + z0442) :|: z1 >= 0, z = 1 + (1 + z0442) + z1, z0442 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U12(mark(z0440), z1254), z1) + MARK(1 + z0440 + z1254) :|: z1254 >= 0, z = 1 + (1 + z0440 + z1254) + z1, z1 >= 0, z0440 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z0439), z1253, z267), z1) + MARK(1 + z0439 + z1253 + z267) :|: z = 1 + (1 + z0439 + z1253 + z267) + z1, z1 >= 0, z1253 >= 0, z0439 >= 0, z267 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z0450), z1) + MARK(1 + z0450) :|: z1 >= 0, z0450 >= 0, z = 1 + (1 + z0450) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__plus(mark(z0435), mark(z1251)), z1) + MARK(1 + z0435 + z1251) :|: z1 >= 0, z0435 >= 0, z1251 >= 0, z = 1 + (1 + z0435 + z1251) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__isNatKind(z0437), z1) + MARK(1 + z0437) :|: z0437 >= 0, z1 >= 0, z = 1 + (1 + z0437) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__isNat(z0429), z1) + MARK(1 + z0429) :|: z = 1 + (1 + z0429) + z1, z1 >= 0, z0429 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__and(mark(z0436), z1252), z1) + MARK(1 + z0436 + z1252) :|: z1 >= 0, z0436 >= 0, z1252 >= 0, z = 1 + (1 + z0436 + z1252) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__U41(mark(z0434), z1250, z266), z1) + MARK(1 + z0434 + z1250 + z266) :|: z1250 >= 0, z1 >= 0, z = 1 + (1 + z0434 + z1250 + z266) + z1, z0434 >= 0, z266 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U31(mark(z0433), z1249), z1) + MARK(1 + z0433 + z1249) :|: z = 1 + (1 + z0433 + z1249) + z1, z0433 >= 0, z1 >= 0, z1249 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U22(mark(z0432)), z1) + MARK(1 + z0432) :|: z1 >= 0, z = 1 + (1 + z0432) + z1, z0432 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U21(mark(z0431), z1248), z1) + MARK(1 + z0431 + z1248) :|: z1 >= 0, z = 1 + (1 + z0431 + z1248) + z1, z0431 >= 0, z1248 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U13(mark(z0430)), z1) + MARK(1 + z0430) :|: z1 >= 0, z = 1 + (1 + z0430) + z1, z0430 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z0428), z1247), z1) + MARK(1 + z0428 + z1247) :|: z1 >= 0, z0428 >= 0, z = 1 + (1 + z0428 + z1247) + z1, z1247 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z0427), z1246, z265), z1) + MARK(1 + z0427 + z1246 + z265) :|: z1 >= 0, z0427 >= 0, z = 1 + (1 + z0427 + z1246 + z265) + z1, z1246 >= 0, z265 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z0438), z1) + MARK(1 + z0438) :|: z1 >= 0, z = 1 + (1 + z0438) + z1, z0438 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z0423), mark(z1244)), z1, z2) + MARK(1 + z0423 + z1244) :|: z = 1 + (1 + z0423 + z1244) + z1 + z2, z1 >= 0, z1244 >= 0, z0423 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__isNatKind(z0425), z1, z2) + MARK(1 + z0425) :|: z1 >= 0, z0425 >= 0, z = 1 + (1 + z0425) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__isNat(z0417), z1, z2) + MARK(1 + z0417) :|: z1 >= 0, z0417 >= 0, z = 1 + (1 + z0417) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__and(mark(z0424), z1245), z1, z2) + MARK(1 + z0424 + z1245) :|: z1 >= 0, z1245 >= 0, z = 1 + (1 + z0424 + z1245) + z1 + z2, z0424 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U41(mark(z0422), z1243, z264), z1, z2) + MARK(1 + z0422 + z1243 + z264) :|: z1 >= 0, z1243 >= 0, z = 1 + (1 + z0422 + z1243 + z264) + z1 + z2, z264 >= 0, z2 >= 0, z0422 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U31(mark(z0421), z1242), z1, z2) + MARK(1 + z0421 + z1242) :|: z1 >= 0, z1242 >= 0, z0421 >= 0, z2 >= 0, z = 1 + (1 + z0421 + z1242) + z1 + z2 MARK(z) -{ 1 }-> 1 + A__U11(a__U22(mark(z0420)), z1, z2) + MARK(1 + z0420) :|: z1 >= 0, z = 1 + (1 + z0420) + z1 + z2, z0420 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z0419), z1241), z1, z2) + MARK(1 + z0419 + z1241) :|: z1 >= 0, z = 1 + (1 + z0419 + z1241) + z1 + z2, z1241 >= 0, z0419 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U13(mark(z0418)), z1, z2) + MARK(1 + z0418) :|: z1 >= 0, z = 1 + (1 + z0418) + z1 + z2, z0418 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z0416), z1240), z1, z2) + MARK(1 + z0416 + z1240) :|: z1 >= 0, z0416 >= 0, z = 1 + (1 + z0416 + z1240) + z1 + z2, z1240 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z0415), z1239, z263), z1, z2) + MARK(1 + z0415 + z1239 + z263) :|: z = 1 + (1 + z0415 + z1239 + z263) + z1 + z2, z1 >= 0, z0415 >= 0, z1239 >= 0, z263 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z0426), z1, z2) + MARK(1 + z0426) :|: z1 >= 0, z0426 >= 0, z2 >= 0, z = 1 + (1 + z0426) + z1 + z2 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__plus(mark(z0867), mark(z1503)), z1) + MARK(1 + z0867 + z1503) :|: z1 >= 0, z0867 >= 0, z = 1 + (1 + z0867 + z1503) + z1, z1503 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0869), z1) + MARK(1 + z0869) :|: z1 >= 0, z0869 >= 0, z = 1 + (1 + z0869) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__isNat(z0861), z1) + MARK(1 + z0861) :|: z1 >= 0, z = 1 + (1 + z0861) + z1, z0861 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z0868), z1504), z1) + MARK(1 + z0868 + z1504) :|: z0868 >= 0, z1 >= 0, z = 1 + (1 + z0868 + z1504) + z1, z1504 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U41(mark(z0866), z1502, z2138), z1) + MARK(1 + z0866 + z1502 + z2138) :|: z1 >= 0, z1502 >= 0, z2138 >= 0, z0866 >= 0, z = 1 + (1 + z0866 + z1502 + z2138) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U31(mark(z0865), z1501), z1) + MARK(1 + z0865 + z1501) :|: z1 >= 0, z1501 >= 0, z = 1 + (1 + z0865 + z1501) + z1, z0865 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U22(mark(z0864)), z1) + MARK(1 + z0864) :|: z = 1 + (1 + z0864) + z1, z0864 >= 0, z1 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U21(mark(z0863), z1500), z1) + MARK(1 + z0863 + z1500) :|: z1 >= 0, z0863 >= 0, z1500 >= 0, z = 1 + (1 + z0863 + z1500) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U13(mark(z0862)), z1) + MARK(1 + z0862) :|: z1 >= 0, z0862 >= 0, z = 1 + (1 + z0862) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__U12(mark(z0860), z1499), z1) + MARK(1 + z0860 + z1499) :|: z0860 >= 0, z1 >= 0, z = 1 + (1 + z0860 + z1499) + z1, z1499 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U11(mark(z0859), z1498, z2137), z1) + MARK(1 + z0859 + z1498 + z2137) :|: z1 >= 0, z2137 >= 0, z1498 >= 0, z = 1 + (1 + z0859 + z1498 + z2137) + z1, z0859 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z0870), z1) + MARK(1 + z0870) :|: z = 1 + (1 + z0870) + z1, z0870 >= 0, z1 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U11(a__and(a__isNatKind(z0871), 1 + z1505), z0871, z1505), z'') :|: z'' >= 0, z = 1, z0871 >= 0, z' = 1 + z0871 + z1505, z1505 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(1, z'') :|: z'' >= 0, z = 1, z' = 0 a__U11(z, z', z'') -{ 0 }-> a__U12(0, z'') :|: z'' >= 0, z = 1, z' >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(1 + z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U11(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U12(z, z') -{ 0 }-> a__U13(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z' - 1 >= 0, z = 1 a__U12(z, z') -{ 0 }-> a__U13(a__U11(a__and(a__isNatKind(z0873), 1 + z1506), z0873, z1506)) :|: z1506 >= 0, z = 1, z' = 1 + z0873 + z1506, z0873 >= 0 a__U12(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U12(z, z') -{ 0 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U12(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U12(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U12(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 1 + z' = v0 a__U12(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 0 = v0 a__U12(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U12(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 1 + z' = z0', z0' >= 0 a__U12(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 0 = z0', z0' >= 0 a__U12(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U13(z) -{ 0 }-> 1 :|: z = 1 a__U13(z) -{ 0 }-> 0 :|: z >= 0 a__U13(z) -{ 0 }-> 1 + z :|: z >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 1, z' - 1 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__and(a__isNatKind(z0875), 1 + z1507), z0875, z1507)) :|: z = 1, z1507 >= 0, z' = 1 + z0875 + z1507, z0875 >= 0 a__U21(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U21(z, z') -{ 0 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U21(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U21(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U21(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 1 + z' = v0 a__U21(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 0 = v0 a__U21(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 1 + z' = z0', z0' >= 0 a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 0 = z0', z0' >= 0 a__U21(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U22(z) -{ 0 }-> 1 :|: z = 1 a__U22(z) -{ 0 }-> 0 :|: z >= 0 a__U22(z) -{ 0 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 0 }-> mark(z') :|: z = 1, z' >= 0 a__U31(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U31(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U41(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z''), mark(z')) :|: z'' >= 0, z = 1, z' >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__and(z, z') -{ 0 }-> mark(z') :|: z = 1, z' >= 0 a__and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__and(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__and(a__isNatKind(z01071), 1 + z1621), 1 + z01071 + z1621) :|: z = 1 + (1 + z01071 + z1621), z01071 >= 0, z1621 >= 0 a__isNat(z) -{ 0 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z01070), 1 + z1), 1 + z01070, z1) :|: z01070 >= 0, z = 1 + (1 + z01070) + z1, z1 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__and(a__isNatKind(z01069), 1 + z1620), 1 + z1), 1 + z01069 + z1620, z1) :|: z1 >= 0, z1620 >= 0, z01069 >= 0, z = 1 + (1 + z01069 + z1620) + z1 a__isNat(z) -{ 0 }-> a__U11(a__and(1, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__U11(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: z >= 0 a__isNat(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNatKind(z) -{ 0 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 0 }-> a__and(a__isNatKind(z01074), 1 + z1) :|: z01074 >= 0, z1 >= 0, z = 1 + (1 + z01074) + z1 a__isNatKind(z) -{ 0 }-> a__and(a__and(a__isNatKind(z01073), 1 + z1622), 1 + z1) :|: z1622 >= 0, z1 >= 0, z01073 >= 0, z = 1 + (1 + z01073 + z1622) + z1 a__isNatKind(z) -{ 0 }-> a__and(1, 1 + (z - 1)) :|: z - 1 >= 0 a__isNatKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: z >= 0 a__isNatKind(z) -{ 0 }-> 1 + z :|: z >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(z' - 2), z' - 2), 1 + (1 + (z' - 2))), 1 + (1 + z) + (1 + z)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z01077), 1 + z1624), z01077, z1624), 1 + (1 + z01077 + z1624)), 1 + (1 + z) + (1 + z)), 1 + z01077 + z1624, z) :|: z1624 >= 0, z' = 1 + (1 + z01077 + z1624), z >= 0, z01077 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + z) + (1 + z)), 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(0, 1 + (z' - 1)), 1 + (1 + z) + (1 + z)), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(1 + (z' - 1), 1 + (z' - 1)), 1 + (1 + z) + (1 + z)), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(z01075), 1 + z1623), z01075, z1623), 1 + (1 + z01075 + z1623)), 1 + z01075 + z1623) :|: z01075 >= 0, z1623 >= 0, z = 1 + z01075 + z1623, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(0, 1 + z), z) :|: z >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U31(a__and(1 + z, 1 + z), z) :|: z >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__plus(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__and(a__plus(mark(z01363), mark(z1791)), z1) :|: z = 1 + (1 + z01363 + z1791) + z1, z1 >= 0, z01363 >= 0, z1791 >= 0 mark(z) -{ 0 }-> a__and(a__isNatKind(z01365), z1) :|: z = 1 + (1 + z01365) + z1, z1 >= 0, z01365 >= 0 mark(z) -{ 0 }-> a__and(a__isNat(z01357), z1) :|: z1 >= 0, z = 1 + (1 + z01357) + z1, z01357 >= 0 mark(z) -{ 0 }-> a__and(a__and(mark(z01364), z1792), z1) :|: z01364 >= 0, z1 >= 0, z = 1 + (1 + z01364 + z1792) + z1, z1792 >= 0 mark(z) -{ 0 }-> a__and(a__U41(mark(z01362), z1790, z2218), z1) :|: z2218 >= 0, z1790 >= 0, z1 >= 0, z = 1 + (1 + z01362 + z1790 + z2218) + z1, z01362 >= 0 mark(z) -{ 0 }-> a__and(a__U31(mark(z01361), z1789), z1) :|: z1 >= 0, z01361 >= 0, z = 1 + (1 + z01361 + z1789) + z1, z1789 >= 0 mark(z) -{ 0 }-> a__and(a__U22(mark(z01360)), z1) :|: z01360 >= 0, z1 >= 0, z = 1 + (1 + z01360) + z1 mark(z) -{ 0 }-> a__and(a__U21(mark(z01359), z1788), z1) :|: z1788 >= 0, z1 >= 0, z = 1 + (1 + z01359 + z1788) + z1, z01359 >= 0 mark(z) -{ 0 }-> a__and(a__U13(mark(z01358)), z1) :|: z1 >= 0, z01358 >= 0, z = 1 + (1 + z01358) + z1 mark(z) -{ 0 }-> a__and(a__U12(mark(z01356), z1787), z1) :|: z1 >= 0, z1787 >= 0, z = 1 + (1 + z01356 + z1787) + z1, z01356 >= 0 mark(z) -{ 0 }-> a__and(a__U11(mark(z01355), z1786, z2217), z1) :|: z1 >= 0, z2217 >= 0, z1786 >= 0, z01355 >= 0, z = 1 + (1 + z01355 + z1786 + z2217) + z1 mark(z) -{ 0 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__and(1 + mark(z01366), z1) :|: z1 >= 0, z01366 >= 0, z = 1 + (1 + z01366) + z1 mark(z) -{ 0 }-> a__U41(a__plus(mark(z01159), mark(z1672)), z1, z2) :|: z1 >= 0, z01159 >= 0, z = 1 + (1 + z01159 + z1672) + z1 + z2, z1672 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__isNatKind(z01161), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01161) + z1 + z2, z01161 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__isNat(z01153), z1, z2) :|: z1 >= 0, z01153 >= 0, z = 1 + (1 + z01153) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__and(mark(z01160), z1673), z1, z2) :|: z = 1 + (1 + z01160 + z1673) + z1 + z2, z1 >= 0, z01160 >= 0, z1673 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U41(mark(z01158), z1671, z2184), z1, z2) :|: z1671 >= 0, z1 >= 0, z01158 >= 0, z = 1 + (1 + z01158 + z1671 + z2184) + z1 + z2, z2184 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U31(mark(z01157), z1670), z1, z2) :|: z1670 >= 0, z1 >= 0, z = 1 + (1 + z01157 + z1670) + z1 + z2, z01157 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U22(mark(z01156)), z1, z2) :|: z1 >= 0, z01156 >= 0, z2 >= 0, z = 1 + (1 + z01156) + z1 + z2 mark(z) -{ 0 }-> a__U41(a__U21(mark(z01155), z1669), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01155 + z1669) + z1 + z2, z1669 >= 0, z01155 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U13(mark(z01154)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z01154) + z1 + z2, z01154 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U12(mark(z01152), z1668), z1, z2) :|: z1668 >= 0, z1 >= 0, z = 1 + (1 + z01152 + z1668) + z1 + z2, z01152 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(a__U11(mark(z01151), z1667, z2183), z1, z2) :|: z1 >= 0, z1667 >= 0, z01151 >= 0, z = 1 + (1 + z01151 + z1667 + z2183) + z1 + z2, z2183 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(1 + mark(z01162), z1, z2) :|: z1 >= 0, z01162 >= 0, z = 1 + (1 + z01162) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U31(a__plus(mark(z01147), mark(z1665)), z1) :|: z = 1 + (1 + z01147 + z1665) + z1, z1 >= 0, z1665 >= 0, z01147 >= 0 mark(z) -{ 0 }-> a__U31(a__isNatKind(z01149), z1) :|: z01149 >= 0, z1 >= 0, z = 1 + (1 + z01149) + z1 mark(z) -{ 0 }-> a__U31(a__isNat(z01141), z1) :|: z = 1 + (1 + z01141) + z1, z01141 >= 0, z1 >= 0 mark(z) -{ 0 }-> a__U31(a__and(mark(z01148), z1666), z1) :|: z1 >= 0, z01148 >= 0, z1666 >= 0, z = 1 + (1 + z01148 + z1666) + z1 mark(z) -{ 0 }-> a__U31(a__U41(mark(z01146), z1664, z2182), z1) :|: z1664 >= 0, z1 >= 0, z = 1 + (1 + z01146 + z1664 + z2182) + z1, z2182 >= 0, z01146 >= 0 mark(z) -{ 0 }-> a__U31(a__U31(mark(z01145), z1663), z1) :|: z01145 >= 0, z1 >= 0, z = 1 + (1 + z01145 + z1663) + z1, z1663 >= 0 mark(z) -{ 0 }-> a__U31(a__U22(mark(z01144)), z1) :|: z1 >= 0, z01144 >= 0, z = 1 + (1 + z01144) + z1 mark(z) -{ 0 }-> a__U31(a__U21(mark(z01143), z1662), z1) :|: z1 >= 0, z1662 >= 0, z = 1 + (1 + z01143 + z1662) + z1, z01143 >= 0 mark(z) -{ 0 }-> a__U31(a__U13(mark(z01142)), z1) :|: z1 >= 0, z = 1 + (1 + z01142) + z1, z01142 >= 0 mark(z) -{ 0 }-> a__U31(a__U12(mark(z01140), z1661), z1) :|: z1 >= 0, z = 1 + (1 + z01140 + z1661) + z1, z01140 >= 0, z1661 >= 0 mark(z) -{ 0 }-> a__U31(a__U11(mark(z01139), z1660, z2181), z1) :|: z1660 >= 0, z2181 >= 0, z1 >= 0, z = 1 + (1 + z01139 + z1660 + z2181) + z1, z01139 >= 0 mark(z) -{ 0 }-> a__U31(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U31(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U31(1 + mark(z01150), z1) :|: z1 >= 0, z = 1 + (1 + z01150) + z1, z01150 >= 0 mark(z) -{ 0 }-> a__U22(a__plus(mark(z01135), mark(z1658))) :|: z01135 >= 0, z1658 >= 0, z = 1 + (1 + z01135 + z1658) mark(z) -{ 0 }-> a__U22(a__isNatKind(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U22(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U22(a__and(mark(z01136), z1659)) :|: z1659 >= 0, z = 1 + (1 + z01136 + z1659), z01136 >= 0 mark(z) -{ 0 }-> a__U22(a__U41(mark(z01134), z1657, z2180)) :|: z01134 >= 0, z1657 >= 0, z2180 >= 0, z = 1 + (1 + z01134 + z1657 + z2180) mark(z) -{ 0 }-> a__U22(a__U31(mark(z01133), z1656)) :|: z = 1 + (1 + z01133 + z1656), z1656 >= 0, z01133 >= 0 mark(z) -{ 0 }-> a__U22(a__U22(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U22(a__U21(mark(z01131), z1655)) :|: z01131 >= 0, z = 1 + (1 + z01131 + z1655), z1655 >= 0 mark(z) -{ 0 }-> a__U22(a__U13(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U22(a__U12(mark(z01128), z1654)) :|: z1654 >= 0, z01128 >= 0, z = 1 + (1 + z01128 + z1654) mark(z) -{ 0 }-> a__U22(a__U11(mark(z01127), z1653, z2179)) :|: z2179 >= 0, z01127 >= 0, z1653 >= 0, z = 1 + (1 + z01127 + z1653 + z2179) mark(z) -{ 0 }-> a__U22(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U21(a__plus(mark(z01123), mark(z1651)), z1) :|: z1 >= 0, z01123 >= 0, z1651 >= 0, z = 1 + (1 + z01123 + z1651) + z1 mark(z) -{ 0 }-> a__U21(a__isNatKind(z01125), z1) :|: z1 >= 0, z = 1 + (1 + z01125) + z1, z01125 >= 0 mark(z) -{ 0 }-> a__U21(a__isNat(z01117), z1) :|: z1 >= 0, z = 1 + (1 + z01117) + z1, z01117 >= 0 mark(z) -{ 0 }-> a__U21(a__and(mark(z01124), z1652), z1) :|: z1 >= 0, z01124 >= 0, z1652 >= 0, z = 1 + (1 + z01124 + z1652) + z1 mark(z) -{ 0 }-> a__U21(a__U41(mark(z01122), z1650, z2178), z1) :|: z2178 >= 0, z1650 >= 0, z1 >= 0, z01122 >= 0, z = 1 + (1 + z01122 + z1650 + z2178) + z1 mark(z) -{ 0 }-> a__U21(a__U31(mark(z01121), z1649), z1) :|: z1 >= 0, z01121 >= 0, z1649 >= 0, z = 1 + (1 + z01121 + z1649) + z1 mark(z) -{ 0 }-> a__U21(a__U22(mark(z01120)), z1) :|: z = 1 + (1 + z01120) + z1, z1 >= 0, z01120 >= 0 mark(z) -{ 0 }-> a__U21(a__U21(mark(z01119), z1648), z1) :|: z1 >= 0, z1648 >= 0, z01119 >= 0, z = 1 + (1 + z01119 + z1648) + z1 mark(z) -{ 0 }-> a__U21(a__U13(mark(z01118)), z1) :|: z = 1 + (1 + z01118) + z1, z1 >= 0, z01118 >= 0 mark(z) -{ 0 }-> a__U21(a__U12(mark(z01116), z1647), z1) :|: z1647 >= 0, z1 >= 0, z = 1 + (1 + z01116 + z1647) + z1, z01116 >= 0 mark(z) -{ 0 }-> a__U21(a__U11(mark(z01115), z1646, z2177), z1) :|: z1 >= 0, z1646 >= 0, z2177 >= 0, z = 1 + (1 + z01115 + z1646 + z2177) + z1, z01115 >= 0 mark(z) -{ 0 }-> a__U21(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U21(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U21(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z01126), z1) :|: z1 >= 0, z = 1 + (1 + z01126) + z1, z01126 >= 0 mark(z) -{ 0 }-> a__U13(a__plus(mark(z01111), mark(z1644))) :|: z = 1 + (1 + z01111 + z1644), z01111 >= 0, z1644 >= 0 mark(z) -{ 0 }-> a__U13(a__isNatKind(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U13(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U13(a__and(mark(z01112), z1645)) :|: z01112 >= 0, z1645 >= 0, z = 1 + (1 + z01112 + z1645) mark(z) -{ 0 }-> a__U13(a__U41(mark(z01110), z1643, z2176)) :|: z1643 >= 0, z01110 >= 0, z = 1 + (1 + z01110 + z1643 + z2176), z2176 >= 0 mark(z) -{ 0 }-> a__U13(a__U31(mark(z01109), z1642)) :|: z = 1 + (1 + z01109 + z1642), z01109 >= 0, z1642 >= 0 mark(z) -{ 0 }-> a__U13(a__U22(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U13(a__U21(mark(z01107), z1641)) :|: z = 1 + (1 + z01107 + z1641), z01107 >= 0, z1641 >= 0 mark(z) -{ 0 }-> a__U13(a__U13(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U13(a__U12(mark(z01104), z1640)) :|: z01104 >= 0, z1640 >= 0, z = 1 + (1 + z01104 + z1640) mark(z) -{ 0 }-> a__U13(a__U11(mark(z01103), z1639, z2175)) :|: z01103 >= 0, z1639 >= 0, z2175 >= 0, z = 1 + (1 + z01103 + z1639 + z2175) mark(z) -{ 0 }-> a__U13(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U12(a__plus(mark(z01099), mark(z1637)), z1) :|: z01099 >= 0, z1 >= 0, z1637 >= 0, z = 1 + (1 + z01099 + z1637) + z1 mark(z) -{ 0 }-> a__U12(a__isNatKind(z01101), z1) :|: z1 >= 0, z = 1 + (1 + z01101) + z1, z01101 >= 0 mark(z) -{ 0 }-> a__U12(a__isNat(z01093), z1) :|: z1 >= 0, z = 1 + (1 + z01093) + z1, z01093 >= 0 mark(z) -{ 0 }-> a__U12(a__and(mark(z01100), z1638), z1) :|: z1 >= 0, z01100 >= 0, z1638 >= 0, z = 1 + (1 + z01100 + z1638) + z1 mark(z) -{ 0 }-> a__U12(a__U41(mark(z01098), z1636, z2174), z1) :|: z2174 >= 0, z01098 >= 0, z1 >= 0, z1636 >= 0, z = 1 + (1 + z01098 + z1636 + z2174) + z1 mark(z) -{ 0 }-> a__U12(a__U31(mark(z01097), z1635), z1) :|: z = 1 + (1 + z01097 + z1635) + z1, z1 >= 0, z1635 >= 0, z01097 >= 0 mark(z) -{ 0 }-> a__U12(a__U22(mark(z01096)), z1) :|: z = 1 + (1 + z01096) + z1, z1 >= 0, z01096 >= 0 mark(z) -{ 0 }-> a__U12(a__U21(mark(z01095), z1634), z1) :|: z1 >= 0, z01095 >= 0, z = 1 + (1 + z01095 + z1634) + z1, z1634 >= 0 mark(z) -{ 0 }-> a__U12(a__U13(mark(z01094)), z1) :|: z = 1 + (1 + z01094) + z1, z1 >= 0, z01094 >= 0 mark(z) -{ 0 }-> a__U12(a__U12(mark(z01092), z1633), z1) :|: z = 1 + (1 + z01092 + z1633) + z1, z1 >= 0, z01092 >= 0, z1633 >= 0 mark(z) -{ 0 }-> a__U12(a__U11(mark(z01091), z1632, z2173), z1) :|: z1 >= 0, z01091 >= 0, z = 1 + (1 + z01091 + z1632 + z2173) + z1, z2173 >= 0, z1632 >= 0 mark(z) -{ 0 }-> a__U12(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U12(1 + mark(z01102), z1) :|: z1 >= 0, z01102 >= 0, z = 1 + (1 + z01102) + z1 mark(z) -{ 0 }-> a__U11(a__plus(mark(z01087), mark(z1630)), z1, z2) :|: z1 >= 0, z1630 >= 0, z2 >= 0, z = 1 + (1 + z01087 + z1630) + z1 + z2, z01087 >= 0 mark(z) -{ 0 }-> a__U11(a__isNatKind(z01089), z1, z2) :|: z1 >= 0, z01089 >= 0, z = 1 + (1 + z01089) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__isNat(z01081), z1, z2) :|: z1 >= 0, z01081 >= 0, z2 >= 0, z = 1 + (1 + z01081) + z1 + z2 mark(z) -{ 0 }-> a__U11(a__and(mark(z01088), z1631), z1, z2) :|: z = 1 + (1 + z01088 + z1631) + z1 + z2, z01088 >= 0, z1 >= 0, z1631 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U41(mark(z01086), z1629, z2172), z1, z2) :|: z1 >= 0, z2172 >= 0, z01086 >= 0, z = 1 + (1 + z01086 + z1629 + z2172) + z1 + z2, z1629 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U31(mark(z01085), z1628), z1, z2) :|: z1 >= 0, z01085 >= 0, z1628 >= 0, z = 1 + (1 + z01085 + z1628) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U22(mark(z01084)), z1, z2) :|: z01084 >= 0, z1 >= 0, z = 1 + (1 + z01084) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U21(mark(z01083), z1627), z1, z2) :|: z1 >= 0, z1627 >= 0, z01083 >= 0, z = 1 + (1 + z01083 + z1627) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U13(mark(z01082)), z1, z2) :|: z1 >= 0, z01082 >= 0, z = 1 + (1 + z01082) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U12(mark(z01080), z1626), z1, z2) :|: z1626 >= 0, z01080 >= 0, z1 >= 0, z = 1 + (1 + z01080 + z1626) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z01079), z1625, z2171), z1, z2) :|: z = 1 + (1 + z01079 + z1625 + z2171) + z1 + z2, z1 >= 0, z1625 >= 0, z2171 >= 0, z01079 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1 + mark(z01090), z1, z2) :|: z = 1 + (1 + z01090) + z1 + z2, z1 >= 0, z01090 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 1 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (69) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U13(v0) -> null_a__U13 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__U11(v0, v1, v2) -> null_A__U11 [0] A__U31(v0, v1) -> null_A__U31 [0] A__U41(v0, v1, v2) -> null_A__U41 [0] A__AND(v0, v1) -> null_A__AND [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__ISNATKIND(v0) -> null_A__ISNATKIND [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] A__U12(v0, v1) -> null_A__U12 [0] A__U21(v0, v1) -> null_A__U21 [0] And the following fresh constants: null_a__U11, null_a__U12, null_a__U13, null_a__U21, null_a__U22, null_a__U31, null_a__U41, null_a__and, null_a__isNat, null_a__isNatKind, null_a__plus, null_mark, null_A__U11, null_A__U31, null_A__U41, null_A__AND, null_A__ISNAT, null_A__ISNATKIND, null_A__PLUS, null_MARK, null_A__U12, null_A__U21 ---------------------------------------- (70) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(MARK(z0)) [1] A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c15(MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) [1] A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c30(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) [1] MARK(s(z0)) -> c41(MARK(z0)) [1] A__U12(tt, z0) -> c2(A__ISNAT(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] MARK(U13(z0)) -> c31(MARK(z0)) [1] MARK(U22(z0)) -> c33(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0) -> a__U13(a__isNat(z0)) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U13(tt) -> tt [0] a__U13(z0) -> U13(z0) [0] a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> mark(z0) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) [0] a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1)) -> a__U12(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U13(z0)) -> a__U13(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U13(v0) -> null_a__U13 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__U11(v0, v1, v2) -> null_A__U11 [0] A__U31(v0, v1) -> null_A__U31 [0] A__U41(v0, v1, v2) -> null_A__U41 [0] A__AND(v0, v1) -> null_A__AND [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__ISNATKIND(v0) -> null_A__ISNATKIND [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] A__U12(v0, v1) -> null_A__U12 [0] A__U21(v0, v1) -> null_A__U21 [0] The TRS has the following type information: A__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c:null_A__U11 tt :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c :: c2:null_A__U12 -> c18:c19:null_A__ISNAT -> c:null_A__U11 A__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c2:null_A__U12 a__isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNAT :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c18:c19:null_A__ISNAT A__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c10:null_A__U31 c10 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c10:null_A__U31 MARK :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK A__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c12:c13:null_A__U41 c12 :: c25:c26:null_A__PLUS -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c12:c13:null_A__U41 A__PLUS :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c25:c26:null_A__PLUS mark :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c13 :: c25:c26:null_A__PLUS -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c12:c13:null_A__U41 A__AND :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c15:null_A__AND c15 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c15:null_A__AND plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c18 :: c:null_A__U11 -> c15:null_A__AND -> c22:c23:null_A__ISNATKIND -> c18:c19:null_A__ISNAT a__and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNATKIND :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c22:c23:null_A__ISNATKIND s :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c19 :: c6:null_A__U21 -> c22:c23:null_A__ISNATKIND -> c18:c19:null_A__ISNAT A__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c6:null_A__U21 c22 :: c15:null_A__AND -> c22:c23:null_A__ISNATKIND -> c22:c23:null_A__ISNATKIND c23 :: c22:c23:null_A__ISNATKIND -> c22:c23:null_A__ISNATKIND 0 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c25 :: c10:null_A__U31 -> c15:null_A__AND -> c18:c19:null_A__ISNAT -> c25:c26:null_A__PLUS c26 :: c12:c13:null_A__U41 -> c15:null_A__AND -> c15:null_A__AND -> c18:c19:null_A__ISNAT -> c25:c26:null_A__PLUS and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c28 :: c:null_A__U11 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c29 :: c2:null_A__U12 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK c30 :: c18:c19:null_A__ISNAT -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c32 :: c6:null_A__U21 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c34 :: c10:null_A__U31 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c35 :: c12:c13:null_A__U41 -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK c36 :: c25:c26:null_A__PLUS -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK c37 :: c25:c26:null_A__PLUS -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK c38 :: c15:null_A__AND -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK c39 :: c22:c23:null_A__ISNATKIND -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK c41 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK c2 :: c18:c19:null_A__ISNAT -> c2:null_A__U12 c6 :: c18:c19:null_A__ISNAT -> c6:null_A__U21 U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c31 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c33 :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK -> c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK a__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U11 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U12 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U13 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U21 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U22 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U31 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U41 :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__and :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNat :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNatKind :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__plus :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_mark :: tt:plus:isNatKind:s:0:isNat:and:U11:U12:U21:U31:U41:U13:U22:null_a__U11:null_a__U12:null_a__U13:null_a__U21:null_a__U22:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_A__U11 :: c:null_A__U11 null_A__U31 :: c10:null_A__U31 null_A__U41 :: c12:c13:null_A__U41 null_A__AND :: c15:null_A__AND null_A__ISNAT :: c18:c19:null_A__ISNAT null_A__ISNATKIND :: c22:c23:null_A__ISNATKIND null_A__PLUS :: c25:c26:null_A__PLUS null_MARK :: c28:c29:c30:c32:c34:c35:c36:c37:c38:c39:c41:c31:c33:null_MARK null_A__U12 :: c2:null_A__U12 null_A__U21 :: c6:null_A__U21 Rewrite Strategy: INNERMOST ---------------------------------------- (71) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__U13 => 0 null_a__U21 => 0 null_a__U22 => 0 null_a__U31 => 0 null_a__U41 => 0 null_a__and => 0 null_a__isNat => 0 null_a__isNatKind => 0 null_a__plus => 0 null_mark => 0 null_A__U11 => 0 null_A__U31 => 0 null_A__U41 => 0 null_A__AND => 0 null_A__ISNAT => 0 null_A__ISNATKIND => 0 null_A__PLUS => 0 null_MARK => 0 null_A__U12 => 0 null_A__U21 => 0 ---------------------------------------- (72) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__ISNAT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0), z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z0), 1 + z1), z0, z1) + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__and(a__isNat(z0), 1 + z0), z0) + A__AND(a__isNat(z0), 1 + z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__and(a__and(a__isNat(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1, z0) + A__AND(a__and(a__isNat(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNat(z1), 1 + z1) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__isNat(z0), z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U12(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U31(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__isNat(z0), z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U12(z, z') -{ 0 }-> a__U13(a__isNat(z0)) :|: z = 1, z0 >= 0, z' = z0 a__U12(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U12(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U13(z) -{ 0 }-> 1 :|: z = 1 a__U13(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U13(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__isNat(z0)) :|: z = 1, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z) -{ 0 }-> 1 :|: z = 1 a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z0), z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z0), 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__and(a__isNatKind(z0), 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U41(a__and(a__and(a__isNat(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U31(a__and(a__isNat(z0), 1 + z0), z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U22(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U13(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U12(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U11(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) by A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3 Compound Symbols: c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3 Compound Symbols: c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt)) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3 Compound Symbols: c10_1, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3 Compound Symbols: c10_1, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt)) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt)) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt)) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0)) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) by A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3 ---------------------------------------- (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__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3 Compound Symbols: c10_1, c15_1, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2 ---------------------------------------- (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__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) by A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) by A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c23_1, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1 Compound Symbols: c10_1, c15_1, c23_1, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) by A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) by MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2 ---------------------------------------- (109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) by MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) by MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2 ---------------------------------------- (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__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) by MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) by MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c36(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c36(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c36(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2 ---------------------------------------- (143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2 ---------------------------------------- (149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) by A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) by A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) by A__U41(tt, U11(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) by A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2)) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt)) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2)) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt)) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2)) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt)) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) by A__U41(tt, isNat(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), 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MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) by A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1)) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt)) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1)) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt)) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1)) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt)) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) by A__U41(tt, U21(x0, z1), x2) -> c12(A__PLUS(mark(x2), U21(mark(x0), z1)), MARK(x2)) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt)) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0)) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), 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A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, 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z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(x0, z1), x2) -> c12(A__PLUS(mark(x2), U21(mark(x0), z1)), MARK(x2)) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt)) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(x0, z1), x2) -> c12(A__PLUS(mark(x2), U21(mark(x0), z1)), MARK(x2)) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt)) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), 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a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) by A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1)) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt)) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1)) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt)) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1)) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt)) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) by A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) by A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) 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U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> 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A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by A__U41(tt, plus(x0, x1), x2) -> c12(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, x1), x2) -> c12(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> 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c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, x1), x2) -> c12(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, 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c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) 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A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, 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c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), 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c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), 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A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), 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z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) by A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), 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0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> 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MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, 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c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), 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c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) 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isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) 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a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), 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x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, 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a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) by A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt)) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0)) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt)) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0)) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> 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a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1)) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt)) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (205) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) by A__U41(tt, U11(z0, z1, z2), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(x1, x2, x3))) A__U41(tt, U12(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U12(mark(z0), z1)), MARK(U11(x1, x2, x3))) A__U41(tt, isNat(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__isNat(z0)), MARK(U11(x1, x2, x3))) A__U41(tt, U13(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U13(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, U21(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U21(mark(z0), z1)), MARK(U11(x1, x2, x3))) A__U41(tt, U22(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U22(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, U31(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U11(x1, x2, x3))) A__U41(tt, U41(z0, z1, z2), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U11(x1, x2, x3))) A__U41(tt, plus(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2, x3))) A__U41(tt, and(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U11(x1, x2, x3))) A__U41(tt, isNatKind(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__isNatKind(z0)), MARK(U11(x1, x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, 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MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, 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c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, 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z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), 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plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) by A__U41(tt, U11(z0, z1, z2), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U12(x1, x2))) A__U41(tt, U12(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U12(x1, x2))) A__U41(tt, isNat(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__isNat(z0)), MARK(U12(x1, x2))) A__U41(tt, U13(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U13(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, U21(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U12(x1, x2))) A__U41(tt, U22(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U22(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, U31(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U12(x1, x2))) A__U41(tt, U41(z0, z1, z2), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U12(x1, x2))) A__U41(tt, plus(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U12(x1, x2))) A__U41(tt, and(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__and(mark(z0), z1)), MARK(U12(x1, x2))) A__U41(tt, isNatKind(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__isNatKind(z0)), MARK(U12(x1, x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2))) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, 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x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, 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a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), 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mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), 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A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, 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z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) by A__U41(tt, U11(z0, z1, z2), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U11(mark(z0), z1, z2)), MARK(isNat(x1))) A__U41(tt, U12(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U12(mark(z0), z1)), MARK(isNat(x1))) A__U41(tt, isNat(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__isNat(z0)), MARK(isNat(x1))) A__U41(tt, U13(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U13(mark(z0))), MARK(isNat(x1))) A__U41(tt, U21(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U21(mark(z0), z1)), MARK(isNat(x1))) A__U41(tt, U22(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U22(mark(z0))), MARK(isNat(x1))) A__U41(tt, U31(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U31(mark(z0), z1)), MARK(isNat(x1))) A__U41(tt, U41(z0, z1, z2), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U41(mark(z0), z1, z2)), MARK(isNat(x1))) A__U41(tt, plus(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__plus(mark(z0), mark(z1))), MARK(isNat(x1))) A__U41(tt, and(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__and(mark(z0), z1)), MARK(isNat(x1))) A__U41(tt, isNatKind(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__isNatKind(z0)), MARK(isNat(x1))) A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), 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A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), 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A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, 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z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (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__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) 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z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), 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A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, 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a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (217) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) by A__U41(tt, U11(z0, z1, z2), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(U13(x1))) A__U41(tt, U12(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U12(mark(z0), z1)), MARK(U13(x1))) A__U41(tt, isNat(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__isNat(z0)), MARK(U13(x1))) A__U41(tt, U13(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U13(mark(z0))), MARK(U13(x1))) A__U41(tt, U21(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U21(mark(z0), z1)), MARK(U13(x1))) A__U41(tt, U22(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U22(mark(z0))), MARK(U13(x1))) A__U41(tt, U31(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U31(mark(z0), z1)), MARK(U13(x1))) A__U41(tt, U41(z0, z1, z2), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U13(x1))) A__U41(tt, plus(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U13(x1))) A__U41(tt, and(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__and(mark(z0), z1)), MARK(U13(x1))) A__U41(tt, isNatKind(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__isNatKind(z0)), MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), tt), MARK(U13(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, tt, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), tt), MARK(U13(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), 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plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> 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c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), 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c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, tt, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), tt), MARK(U13(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (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__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, 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A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), 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A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), 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x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (221) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) by A__U41(tt, U11(z0, z1, z2), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U21(x1, x2))) A__U41(tt, U12(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U21(x1, x2))) A__U41(tt, isNat(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__isNat(z0)), MARK(U21(x1, x2))) A__U41(tt, U13(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U13(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, U21(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U21(x1, x2))) A__U41(tt, U22(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U22(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, U31(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U21(x1, x2))) A__U41(tt, U41(z0, z1, z2), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U21(x1, x2))) A__U41(tt, plus(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U21(x1, x2))) A__U41(tt, and(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__and(mark(z0), z1)), MARK(U21(x1, x2))) A__U41(tt, isNatKind(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__isNatKind(z0)), MARK(U21(x1, x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), tt), MARK(U21(x1, x2))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2))) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> 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c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), tt), MARK(U21(x1, x2))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), tt), MARK(U21(x1, x2))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> 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c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> 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A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 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0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, 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c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) by A__U41(tt, U11(z0, z1, z2), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(U22(x1))) A__U41(tt, U12(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U12(mark(z0), z1)), MARK(U22(x1))) A__U41(tt, isNat(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__isNat(z0)), MARK(U22(x1))) A__U41(tt, U13(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U13(mark(z0))), MARK(U22(x1))) A__U41(tt, U21(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U21(mark(z0), z1)), MARK(U22(x1))) A__U41(tt, U22(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U22(mark(z0))), MARK(U22(x1))) A__U41(tt, U31(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U31(mark(z0), z1)), MARK(U22(x1))) A__U41(tt, U41(z0, z1, z2), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U22(x1))) A__U41(tt, plus(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U22(x1))) A__U41(tt, and(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__and(mark(z0), z1)), MARK(U22(x1))) A__U41(tt, isNatKind(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__isNatKind(z0)), MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), 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A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), 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c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (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__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> 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MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> 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A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (229) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) by A__U41(tt, U11(z0, z1, z2), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U31(x1, x2))) A__U41(tt, U12(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U31(x1, x2))) A__U41(tt, isNat(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__isNat(z0)), MARK(U31(x1, x2))) A__U41(tt, U13(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U13(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, U21(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U31(x1, x2))) A__U41(tt, U22(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U22(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, U31(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U31(x1, x2))) A__U41(tt, U41(z0, z1, z2), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U31(x1, x2))) A__U41(tt, plus(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U31(x1, x2))) A__U41(tt, and(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__and(mark(z0), z1)), MARK(U31(x1, x2))) A__U41(tt, isNatKind(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__isNatKind(z0)), MARK(U31(x1, x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), 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c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), 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A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), 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z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> 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MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), 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0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> 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MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, 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c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), 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A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (231) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, 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A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (233) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) by A__U41(tt, U11(z0, z1, z2), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U41(x1, x2, x3))) A__U41(tt, U12(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U12(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U41(tt, isNat(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__isNat(z0)), MARK(U41(x1, x2, x3))) A__U41(tt, U13(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U13(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, U21(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U21(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U41(tt, U22(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U22(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, U31(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U41(tt, U41(z0, z1, z2), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U41(x1, x2, x3))) A__U41(tt, plus(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U41(x1, x2, x3))) A__U41(tt, and(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U41(tt, isNatKind(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__isNatKind(z0)), MARK(U41(x1, x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> 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z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, 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plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, 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MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, 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U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), 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A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, 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z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) 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A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, 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x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), 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c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (237) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by A__U41(tt, U11(z0, z1, z2), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U41(tt, U12(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0), z1)), MARK(plus(x1, x2))) A__U41(tt, isNat(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNat(z0)), MARK(plus(x1, x2))) A__U41(tt, U13(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U13(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, U21(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0), z1)), MARK(plus(x1, x2))) A__U41(tt, U22(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U22(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, U31(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U31(mark(z0), z1)), MARK(plus(x1, x2))) A__U41(tt, U41(z0, z1, z2), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U41(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U41(tt, plus(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2))) A__U41(tt, and(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__and(mark(z0), z1)), MARK(plus(x1, x2))) A__U41(tt, isNatKind(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNatKind(z0)), MARK(plus(x1, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) 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A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) 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z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), 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a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, 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mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> 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x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (239) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), 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x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), 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A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, 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c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, 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z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (241) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) by A__U41(tt, U11(z0, z1, z2), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(and(x1, x2))) A__U41(tt, U12(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U12(mark(z0), z1)), MARK(and(x1, x2))) A__U41(tt, isNat(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__isNat(z0)), MARK(and(x1, x2))) A__U41(tt, U13(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U13(mark(z0))), MARK(and(x1, x2))) A__U41(tt, U21(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U21(mark(z0), z1)), MARK(and(x1, x2))) A__U41(tt, U22(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U22(mark(z0))), MARK(and(x1, x2))) A__U41(tt, U31(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U31(mark(z0), z1)), MARK(and(x1, x2))) A__U41(tt, U41(z0, z1, z2), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(and(x1, x2))) A__U41(tt, plus(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(and(x1, x2))) A__U41(tt, and(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__and(mark(z0), z1)), MARK(and(x1, x2))) A__U41(tt, isNatKind(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__isNatKind(z0)), MARK(and(x1, x2))) A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), 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mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), 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c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> 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MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, 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U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2 ---------------------------------------- (243) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0) -> a__U13(a__isNat(z0)) a__U12(z0, z1) -> U12(z0, z1) a__U13(tt) -> tt a__U13(z0) -> U13(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1)) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0) a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U13(z0)) -> a__U13(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> 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z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U41(tt, isNat(0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0))) A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0))) A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1)) A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1)) A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1)) A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1)) A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0))) A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0))) A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0))) A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0))) A__U41(tt, U13(x0), x1) -> c12(MARK(x1)) A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0)))) A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0)))) A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2)) A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2)) A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1))) A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1))) A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1)) A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1)) A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1)) A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1)) A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1)) A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1)) A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1)) A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1)) A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2))) A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1))) A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0))) A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0))) A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1))) A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0))) A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1))) A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2))) A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1))) A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1))) A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0))) A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0))) A__U41(tt, U22(x0), x1) -> c12(MARK(x1)) A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0)))) A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0)))) A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> 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MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c10(MARK(z0)) A__AND(tt, z0) -> c15(MARK(z0)) A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c30(A__ISNAT(z0)) MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0)) MARK(s(z0)) -> c41(MARK(z0)) A__U12(tt, z0) -> c2(A__ISNAT(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) MARK(U13(z0)) -> c31(MARK(z0)) MARK(U22(z0)) -> c33(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, x1)) A__U11(tt, z0, x1) -> c(A__ISNAT(z0)) A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1)) A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U41(tt, tt, x1) -> c12(MARK(x1)) A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0))) A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0))) A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0))) A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0))) A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0)) A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0)) A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0)) A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0)) A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1))) A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c19(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1))) A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0)) A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0))) A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0))) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U12(tt, x1)) -> c29(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c29(MARK(s(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(tt, x1)) -> c32(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c32(MARK(s(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(tt, x1)) -> c34(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c34(MARK(s(z0))) MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1))) MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0))) MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c36(MARK(x0)) MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0))) MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0))) MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(tt, x1)) -> c38(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c38(MARK(s(z0))) A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1))) A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2))) A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1))) A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2)) A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2)) A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1))) A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1))) A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1)) A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1)) A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1))) A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0))) A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1))) A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0))) A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0))) A__U41(tt, isNat(x0), s(z0)) -> 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A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1))) A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1))) A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3)) A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0))) A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1))) A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0))) A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0))) A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3)) A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2)) A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2)) A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1))) A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0))) A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1))) A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0))) A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0))) A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2)) A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2)) A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2))) A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1))) A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0))) A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1))) A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0))) A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1))) A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0))) A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2)) A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1))) A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1))) A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1)) A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2))) A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1))) A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0))) A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0))) A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1))) A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0))) A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1))) A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2))) A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1))) A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1))) A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0))) A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0))) A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1)) A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0))) A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0))) A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3))) A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3))) A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3))) A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3))) A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3))) A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3))) A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3))) A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3))) A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2))) A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2))) A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1))) A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2))) A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2))) A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2))) A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2))) A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2))) A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2))) A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2))) A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2))) A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2))) A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2))) A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2))) A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2))) A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2))) A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2))) A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0))) A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0)))) A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1))) A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1))) A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1))) A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1))) A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2)))) A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1)))) A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0)))) A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0)))) A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1)))) A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0)))) A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1)))) A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2)))) A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1)))) A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1)))) A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0)))) A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt))) A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0)))) A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0))) A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1))) A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2))) A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2))) A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1))) A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2))) A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2))) A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2))) A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2))) A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2))) A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2))) A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2))) A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2))) A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2))) A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2))) A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2))) A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2))) A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2))) A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2))) A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0))) A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1))) A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1))) A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1))) A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2)))) A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1)))) A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0)))) A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0)))) A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1)))) A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0)))) A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1)))) A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2)))) A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1)))) A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1)))) A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0)))) A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt))) A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0)))) A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0))) A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1))) A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2))) A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2))) A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2))) A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2))) A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2))) A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2))) A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2))) A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2))) A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0))) A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3))) A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3))) A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3))) A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3))) A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3))) A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3))) A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1)))) A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0)))) A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1)))) A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0)))) A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0)))) A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2))) A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2))) A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2))) A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2))) A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2))) A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2))) A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2))) A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2))) A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2))) A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2))) A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2))) A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2))) A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2))) A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2))) A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2))) A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2